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University of Georgia
1.
Hannah, Mark Edward.
An analysis of the three body problem.
Degree: 2014, University of Georgia
URL: http://hdl.handle.net/10724/29188
► In this paper we will be presenting my approach to generating two possible solutions to the three-body problem. We will first discuss the theory of…
(more)
▼ In this paper we will be presenting my approach to generating two possible solutions to the three-body problem. We will first discuss the theory of reducing the dimension of the dynamical system through the use of symmetry and constants of
motion. However, we can reduce no farther than to 5 degrees of freedom, which is still too high to solve and therefore we must change our attack from trying to find a general solution, to simply finding a specific solution.|We will then make use of the
program Maple, which will allow me to create a simulation of this system. Through the simulations we will try and find the stable figure eight solution as well as a solution having a light satellite coming in from infinity and being captured in a stable
orbit around a tight binary. We can adjust the initial conditions of the three bodies until we have generated a simulation that has the potential to be a stable periodic orbit. Unfortunately Maple will not prove that any solution found is stable, and we
are therefore left with only a conjecture as to the stability of the system.
Subjects/Keywords: Celestial Mechanics; n-Body Problem; Three-body Problem; 3-Body Problem
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APA (6^{th} Edition):
Hannah, M. E. (2014). An analysis of the three body problem. (Thesis). University of Georgia. Retrieved from http://hdl.handle.net/10724/29188
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16^{th} Edition):
Hannah, Mark Edward. “An analysis of the three body problem.” 2014. Thesis, University of Georgia. Accessed October 30, 2020.
http://hdl.handle.net/10724/29188.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7^{th} Edition):
Hannah, Mark Edward. “An analysis of the three body problem.” 2014. Web. 30 Oct 2020.
Vancouver:
Hannah ME. An analysis of the three body problem. [Internet] [Thesis]. University of Georgia; 2014. [cited 2020 Oct 30].
Available from: http://hdl.handle.net/10724/29188.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Hannah ME. An analysis of the three body problem. [Thesis]. University of Georgia; 2014. Available from: http://hdl.handle.net/10724/29188
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Johannesburg
2.
Anderson, Keegan Doig.
Gravitational capture.
Degree: 2012, University of Johannesburg
URL: http://hdl.handle.net/10210/8053
► M.Sc.
Important ideas from dynamical systems theory and the restricted three-body problem are introduced. The intention is the application of dynamical systems theory techniques to…
(more)
▼ M.Sc.
Important ideas from dynamical systems theory and the restricted three-body problem are introduced. The intention is the application of dynamical systems theory techniques to the restricted three-body problem to better understand the phenomenon of gravitational capture. Chapter 1 gives a much deeper review of the purpose of this dissertation. Chapter 2 introduces and reviews important concepts from dynamical systems. Chapter 3 reviews the restricted three-body problem and all important aspects of the problem. In chapter 4 we define and study the phenomenon of gravitational capture. We take a novel approach by applying a symplectic method, namely the implicit midpoint method, to model trajectories in the restricted three-body problem. As far as we know, this is the first time such a method has actually been applied, with other authors preferring to apply explicit methods in trajectory modelling. In the closing of this chapter we review our whole discourse and suggest topics for future research. The disseration is concluded with two appendix chapters. In the first chapter we list all the computer code we have written for this dissertation. The second appendix chapter reviews the n-body problem and we show a full solution of the two-body problem.
Subjects/Keywords: Gravitation; Space trajectories; Dynamics; Three-body problem; Two-body problem
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APA (6^{th} Edition):
Anderson, K. D. (2012). Gravitational capture. (Thesis). University of Johannesburg. Retrieved from http://hdl.handle.net/10210/8053
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16^{th} Edition):
Anderson, Keegan Doig. “Gravitational capture.” 2012. Thesis, University of Johannesburg. Accessed October 30, 2020.
http://hdl.handle.net/10210/8053.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7^{th} Edition):
Anderson, Keegan Doig. “Gravitational capture.” 2012. Web. 30 Oct 2020.
Vancouver:
Anderson KD. Gravitational capture. [Internet] [Thesis]. University of Johannesburg; 2012. [cited 2020 Oct 30].
Available from: http://hdl.handle.net/10210/8053.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Anderson KD. Gravitational capture. [Thesis]. University of Johannesburg; 2012. Available from: http://hdl.handle.net/10210/8053
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of British Columbia
3.
Hamilton, Rognvald Thore.
The limiting case of periodic orbits near the lagrangian equilateral triangle solutions of the restricted three body problem.
Degree: MA- MA, Mathematics, 1939, University of British Columbia
URL: http://hdl.handle.net/2429/38714
[No abstract available]
Subjects/Keywords: Three-body problem
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APA (6^{th} Edition):
Hamilton, R. T. (1939). The limiting case of periodic orbits near the lagrangian equilateral triangle solutions of the restricted three body problem. (Masters Thesis). University of British Columbia. Retrieved from http://hdl.handle.net/2429/38714
Chicago Manual of Style (16^{th} Edition):
Hamilton, Rognvald Thore. “The limiting case of periodic orbits near the lagrangian equilateral triangle solutions of the restricted three body problem.” 1939. Masters Thesis, University of British Columbia. Accessed October 30, 2020.
http://hdl.handle.net/2429/38714.
MLA Handbook (7^{th} Edition):
Hamilton, Rognvald Thore. “The limiting case of periodic orbits near the lagrangian equilateral triangle solutions of the restricted three body problem.” 1939. Web. 30 Oct 2020.
Vancouver:
Hamilton RT. The limiting case of periodic orbits near the lagrangian equilateral triangle solutions of the restricted three body problem. [Internet] [Masters thesis]. University of British Columbia; 1939. [cited 2020 Oct 30].
Available from: http://hdl.handle.net/2429/38714.
Council of Science Editors:
Hamilton RT. The limiting case of periodic orbits near the lagrangian equilateral triangle solutions of the restricted three body problem. [Masters Thesis]. University of British Columbia; 1939. Available from: http://hdl.handle.net/2429/38714
The Ohio State University
4.
Jedrey, Richard M.
Development of a Discretized Model for the Restricted
Three-Body Problem.
Degree: MS, Aero/Astro Engineering, 2011, The Ohio State University
URL: http://rave.ohiolink.edu/etdc/view?acc_num=osu1306856595
► Spacecraft trajectory design is a science that requires high precision with little error. One of the most classic trajectory design problems is the restricted three-body…
(more)
▼ Spacecraft trajectory design is a science that
requires high precision with little error. One of the most classic
trajectory design problems is the restricted
three-
body problem.
Two methods to develop the trajectory of a spacecraft under the
influence of two celestial bodies are through the use of the
equations of motion, and the patched-conic approximation. Popular
tools such as MATLAB can be used to solve the equations of motion
if great care is taken when selecting an ODE solver since the
results are dramatically different between different solvers. As a
result, these tools aren’t very robust and can create significant
errors, so a different approach must be used for generalized
scenarios when an exact solution for comparison is unavailable. The
patched-conic approximation can be easily used in a program such as
MATLAB, but its exclusion of one of the two celestial bodies at
every point in the trajectory creates drawbacks and significant
errors. To avoid the errors that exist when using the patched-conic
approach, research was put into the development of a simple model
that could propagate a spacecraft’s trajectory under the effect of
two celestial bodies while being robust enough to code and solve in
a widely available program such as MATLAB. This model acts as a
modification to the patched-conic approach. Throughout the
trajectory the effect of the primary celestial
body of the system
on the spacecraft was calculated, as in the patched-conic approach,
however unlike the patched-conic approach this effect is not
ignored when the spacecraft reaches the secondary body’s sphere of
influence. Furthermore, the effect of the secondary
body was also
considered even when the spacecraft is outside the secondary body’s
sphere of influence. Then, by applying a weighted average to the
spacecraft’s radius and velocity components respective to each
celestial
body, an updated state would be created that would allow
the model to accurately propagate the trajectory. This would be
compared to a numerically generated ‘exact’ solution to determine
the errors. Algorithms that propagate the spacecraft’s trajectory
out with respect to both celestial bodies were created and tested,
including the propagation of the secondary celestial body’s orbit
itself. A scheme based on the geometry was used in an attempt to
combine the spacecraft’s states with respect to both celestial
bodies using a weighted average. This scheme was tested at multiple
points throughout the trajectory using a variety of weights, but no
attempts were met with any success. However, the routines
propagating the trajectories of the celestial bodies and spacecraft
were proven to work correctly, and an initial foundation in
creating a scheme to combine the spacecraft’s state has been laid
out.
Advisors/Committee Members: Oz, Hayrani (Advisor).
Subjects/Keywords: Aerospace Engineering; Engineering; orbital mechanics; spacecraft trajectories; three-body problem; three-body model; n-body problem; n-body model; discretized spacecraft
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APA ·
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APA (6^{th} Edition):
Jedrey, R. M. (2011). Development of a Discretized Model for the Restricted
Three-Body Problem. (Masters Thesis). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1306856595
Chicago Manual of Style (16^{th} Edition):
Jedrey, Richard M. “Development of a Discretized Model for the Restricted
Three-Body Problem.” 2011. Masters Thesis, The Ohio State University. Accessed October 30, 2020.
http://rave.ohiolink.edu/etdc/view?acc_num=osu1306856595.
MLA Handbook (7^{th} Edition):
Jedrey, Richard M. “Development of a Discretized Model for the Restricted
Three-Body Problem.” 2011. Web. 30 Oct 2020.
Vancouver:
Jedrey RM. Development of a Discretized Model for the Restricted
Three-Body Problem. [Internet] [Masters thesis]. The Ohio State University; 2011. [cited 2020 Oct 30].
Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1306856595.
Council of Science Editors:
Jedrey RM. Development of a Discretized Model for the Restricted
Three-Body Problem. [Masters Thesis]. The Ohio State University; 2011. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1306856595
University of British Columbia
5.
Barkham, Peter George Douglas.
Some aspects of three and four-body dynamics.
Degree: PhD, Electrical and Computer Engineering, 1974, University of British Columbia
URL: http://hdl.handle.net/2429/18937
► Two fundamental problems of celestial mechanics are considered: the stellar or planetary three-body problem and a related form of the restricted four-body problem. Although a…
(more)
▼ Two fundamental problems of celestial mechanics are considered: the stellar or planetary three-body problem and a related form of the restricted four-body problem. Although a number of constraints are imposed, no assumptions are made which could invalidate the final solution. A consistent and rational approach to the analysis of four-body systems has not previously been developed, and an attempt is made here to describe problem evolution in a systematic manner. In the particular three-body problem under consideration two masses, forming a close binary system, orbit a comparatively distant mass. A new literal, periodic solution of this problem is found in terms of a small parameter e, which is related to the distance separating the binary system and the remaining mass, using the two variable expansion procedure. The solution is accurate within a constant error O(e¹¹) and uniformly valid as e tends to zero for time intervals 0(e¹⁴). Two specific examples are chosen to verify the literal solution, one of which relates to the sun-earth-moon configuration of the solar system. The second example applies to a problem of stellar motion where the three masses are in the ratio 20 : 1 : 1. In both cases a comparison of the analytical solution with an equivalent numerically-generated orbit shows .close agreement, with an error below 5 percent for the sun-earth-moon configuration and less than 3 percent for the stellar system.
The four-body problem is derived from the three-body case by introducing a particle of negligible mass into the close binary system. Unique uniformly valid solutions are found for motion near both equilateral triangle points of the binary system in terms of the small parameter e, where the primaries move in accordance with the uniformly-valid three-body solution. Accuracy, in this case, is Q maintained within a constant error 0(e⁸), and the solutions are uniformly
valid as e tends to zero for time intervals 0(e¹¹). Orbital position errors near L₄ and L₅ of the earth-moon system are found to be less than 5 percent when numerically-generated periodic solutions are used as a standard of comparison.
The approach described here should, in general, be useful in the analysis of non-integrable dynamic systems, particularly when it is feasible to decompose the problem into a number of subsidiary cases.
Subjects/Keywords: Two-body problem; Three-body problem
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APA (6^{th} Edition):
Barkham, P. G. D. (1974). Some aspects of three and four-body dynamics. (Doctoral Dissertation). University of British Columbia. Retrieved from http://hdl.handle.net/2429/18937
Chicago Manual of Style (16^{th} Edition):
Barkham, Peter George Douglas. “Some aspects of three and four-body dynamics.” 1974. Doctoral Dissertation, University of British Columbia. Accessed October 30, 2020.
http://hdl.handle.net/2429/18937.
MLA Handbook (7^{th} Edition):
Barkham, Peter George Douglas. “Some aspects of three and four-body dynamics.” 1974. Web. 30 Oct 2020.
Vancouver:
Barkham PGD. Some aspects of three and four-body dynamics. [Internet] [Doctoral dissertation]. University of British Columbia; 1974. [cited 2020 Oct 30].
Available from: http://hdl.handle.net/2429/18937.
Council of Science Editors:
Barkham PGD. Some aspects of three and four-body dynamics. [Doctoral Dissertation]. University of British Columbia; 1974. Available from: http://hdl.handle.net/2429/18937
Texas A&M University
6.
Kim, Hyerim.
Advanced Mission Design: Interplanetary Super Highway Trajectory Method.
Degree: PhD, Aerospace Engineering, 2015, Texas A&M University
URL: http://hdl.handle.net/1969.1/155436
► Near-future space missions demand the delivery of massive payloads to deep space destinations. Given foreseeable propulsion technology, this is feasible only if we can design…
(more)
▼ Near-future space missions demand the delivery of massive payloads to deep space destinations. Given foreseeable propulsion technology, this is feasible only if we can design trajectories that require the smallest possible propulsive energy input. This research aims to design interplanetary space missions by using new low-energy trajectory methods that take advantage of natural dynamics in the solar system. This energy efficient trajectory technology, called the Interplanetary Super Highway (IPSH), allows long duration space missions with minimum fuel requirements. To develop the IPSH trajectory design method, invariant manifolds of the
three-
body problem are used. The invariant manifolds, which are tube-like structures that issue from the periodic orbits around the L1 and L2 Lagrangian points, can be patched together to achieve voyages of immense distances while the spacecraft expends little or no energy. This patched
three-
body method of trajectory design is fairly well developed for impulsive propulsion. My research is dedicated to advance its capabilities by extending it to continuous, low-thrust, high specific impulse propulsion methods.
The IPSH trajectory design method would be useful in designing many types of interplanetary missions. As one of its applications, my research is focused on Near-Earth Asteroids (NEAs) rendezvous mission design for exploration, mitigation, and mining. Asteroids have many valuable resources such as minerals and volatiles, which can be brought back to Earth or used in space for propulsion systems or space habitats and stations. Transportation to and from asteroids will require relatively massive vehicles capable of sustaining crew for long durations while economizing on propellant mass. Thus, in the design of advanced NEA rendezvous missions, developing new technology for low cost trajectories will play a key role.
In a second application study, the solar sail mission for Mars exploration is considered. By using solar radiation pressure, solar sails provide propulsive power. This thrust affects the
three-
body system dynamics such that the Sun-Mars L1 and L2 Lagrangian points are shifted toward the Sun and the geometry of the invariant manifolds around L1 and L2 points is changed. By taking advantage of these features, a low-thrust trajectory for Mars exploration is developed.
Advisors/Committee Members: Hyland, David C. (advisor), Vadali, Srinivas Rao (committee member), Pollock, Tom (committee member), Macri, Lucas (committee member).
Subjects/Keywords: low thrust trajectory; interplanetary super highway; three body problem
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APA (6^{th} Edition):
Kim, H. (2015). Advanced Mission Design: Interplanetary Super Highway Trajectory Method. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/155436
Chicago Manual of Style (16^{th} Edition):
Kim, Hyerim. “Advanced Mission Design: Interplanetary Super Highway Trajectory Method.” 2015. Doctoral Dissertation, Texas A&M University. Accessed October 30, 2020.
http://hdl.handle.net/1969.1/155436.
MLA Handbook (7^{th} Edition):
Kim, Hyerim. “Advanced Mission Design: Interplanetary Super Highway Trajectory Method.” 2015. Web. 30 Oct 2020.
Vancouver:
Kim H. Advanced Mission Design: Interplanetary Super Highway Trajectory Method. [Internet] [Doctoral dissertation]. Texas A&M University; 2015. [cited 2020 Oct 30].
Available from: http://hdl.handle.net/1969.1/155436.
Council of Science Editors:
Kim H. Advanced Mission Design: Interplanetary Super Highway Trajectory Method. [Doctoral Dissertation]. Texas A&M University; 2015. Available from: http://hdl.handle.net/1969.1/155436
Michigan State University
7.
Larson, Nancy Marie Zander, 1946-.
Three-body problem : a formalism and computer code for arbitrary kinds of particles.
Degree: PhD, Department of Physics, 1972, Michigan State University
URL: http://etd.lib.msu.edu/islandora/object/etd:18893
Subjects/Keywords: Three-body problem; Nuclear physics
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APA (6^{th} Edition):
Larson, Nancy Marie Zander, 1. (1972). Three-body problem : a formalism and computer code for arbitrary kinds of particles. (Doctoral Dissertation). Michigan State University. Retrieved from http://etd.lib.msu.edu/islandora/object/etd:18893
Chicago Manual of Style (16^{th} Edition):
Larson, Nancy Marie Zander, 1946-. “Three-body problem : a formalism and computer code for arbitrary kinds of particles.” 1972. Doctoral Dissertation, Michigan State University. Accessed October 30, 2020.
http://etd.lib.msu.edu/islandora/object/etd:18893.
MLA Handbook (7^{th} Edition):
Larson, Nancy Marie Zander, 1946-. “Three-body problem : a formalism and computer code for arbitrary kinds of particles.” 1972. Web. 30 Oct 2020.
Vancouver:
Larson, Nancy Marie Zander 1. Three-body problem : a formalism and computer code for arbitrary kinds of particles. [Internet] [Doctoral dissertation]. Michigan State University; 1972. [cited 2020 Oct 30].
Available from: http://etd.lib.msu.edu/islandora/object/etd:18893.
Council of Science Editors:
Larson, Nancy Marie Zander 1. Three-body problem : a formalism and computer code for arbitrary kinds of particles. [Doctoral Dissertation]. Michigan State University; 1972. Available from: http://etd.lib.msu.edu/islandora/object/etd:18893
Boston University
8.
Atanasova, Diana.
Transit orbits and long-term dynamics in the near-parabolic restricted three-body problems.
Degree: PhD, Mathematics & Statistics, 2020, Boston University
URL: http://hdl.handle.net/2144/39615
► In this thesis, we consider the planar parabolic, hyperbolic, and highly-elliptic restricted three-body problems (R3BP). In particular, we formulate sufficient conditions for no transit (escape…
(more)
▼ In this thesis, we consider the planar parabolic, hyperbolic, and highly-elliptic restricted
three-
body problems (R3BP). In particular, we formulate sufficient conditions for no transit (escape of the infinitesimal
body) to occur in the near-parabolic R3BP using the disturbing function derived in Mamedov (1987) as our starting point. We take a middle approach between purely numerical and strictly analytic in the form of infinite series expansions to derive approximation mappings modeling the dynamics. Motivated by the long-term dynamics of the highly-elliptic R3BP, we study an annulus map with properties which are unexpectedly different from those of the "standard" annulus map.
Advisors/Committee Members: Hall, Glen R. (advisor).
Subjects/Keywords: Mathematics; Annulus map; Parabolic restricted three-body problem; Transit orbits
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APA ·
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APA (6^{th} Edition):
Atanasova, D. (2020). Transit orbits and long-term dynamics in the near-parabolic restricted three-body problems. (Doctoral Dissertation). Boston University. Retrieved from http://hdl.handle.net/2144/39615
Chicago Manual of Style (16^{th} Edition):
Atanasova, Diana. “Transit orbits and long-term dynamics in the near-parabolic restricted three-body problems.” 2020. Doctoral Dissertation, Boston University. Accessed October 30, 2020.
http://hdl.handle.net/2144/39615.
MLA Handbook (7^{th} Edition):
Atanasova, Diana. “Transit orbits and long-term dynamics in the near-parabolic restricted three-body problems.” 2020. Web. 30 Oct 2020.
Vancouver:
Atanasova D. Transit orbits and long-term dynamics in the near-parabolic restricted three-body problems. [Internet] [Doctoral dissertation]. Boston University; 2020. [cited 2020 Oct 30].
Available from: http://hdl.handle.net/2144/39615.
Council of Science Editors:
Atanasova D. Transit orbits and long-term dynamics in the near-parabolic restricted three-body problems. [Doctoral Dissertation]. Boston University; 2020. Available from: http://hdl.handle.net/2144/39615
Rutgers University
9.
Trim, Nkosi Nathan.
Visualizing solutions of the circular restricted three-body problem.
Degree: MS, Mathematical Sciences, 2009, Rutgers University
URL: http://hdl.rutgers.edu/1782.2/rucore10005600001.ETD.000051338
► The stability of a satellite near the Lagrange points is studied in a Circular Restricted Three-Body Problem (CR3BP). The Runge Kutta method is used to…
(more)
▼ The stability of a satellite near the Lagrange points is studied in a Circular Restricted
Three-
Body Problem (CR3BP). The Runge Kutta method is used to trace out the orbital path of the satellite over a period of time. Various initial positions near the Lagrange points and velocities are used to produce various paths the satellite can take. The primary paths focused are on horseshoe paths.
Horseshoe orbits are shown to be sometimes stable and sometimes chaotic.
Advisors/Committee Members: Trim, Nkosi Nathan (author), Herrera-Guzman, Haydee (chair).
Subjects/Keywords: Three-body problem; Celestial mechanics
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APA (6^{th} Edition):
Trim, N. N. (2009). Visualizing solutions of the circular restricted three-body problem. (Masters Thesis). Rutgers University. Retrieved from http://hdl.rutgers.edu/1782.2/rucore10005600001.ETD.000051338
Chicago Manual of Style (16^{th} Edition):
Trim, Nkosi Nathan. “Visualizing solutions of the circular restricted three-body problem.” 2009. Masters Thesis, Rutgers University. Accessed October 30, 2020.
http://hdl.rutgers.edu/1782.2/rucore10005600001.ETD.000051338.
MLA Handbook (7^{th} Edition):
Trim, Nkosi Nathan. “Visualizing solutions of the circular restricted three-body problem.” 2009. Web. 30 Oct 2020.
Vancouver:
Trim NN. Visualizing solutions of the circular restricted three-body problem. [Internet] [Masters thesis]. Rutgers University; 2009. [cited 2020 Oct 30].
Available from: http://hdl.rutgers.edu/1782.2/rucore10005600001.ETD.000051338.
Council of Science Editors:
Trim NN. Visualizing solutions of the circular restricted three-body problem. [Masters Thesis]. Rutgers University; 2009. Available from: http://hdl.rutgers.edu/1782.2/rucore10005600001.ETD.000051338
University of British Columbia
10.
Banville, Marcel Roland.
A variational wave function for the ground state of He³, and its application to the D(p,y)He³ capture reaction.
Degree: PhD, Physics, 1965, University of British Columbia
URL: http://hdl.handle.net/2429/38375
► The present work proposes trial wave functions for the three-body problem in nuclear physics taking into account the group theoretical classification of the states given…
(more)
▼ The present work proposes trial wave functions for the three-body problem in nuclear physics taking into account the group theoretical classification of the states given by Derrick and Blatt and by Verde. We start from the Schroedinger equation in the internal variables (the interparticle distances) obtained by Derrick from a summation over the matrix elements for kinetic energy and potential energy extended over all variables except the internal variables.
An “equivalent" Schroedinger equation is set up using a potential due to Eckart. This equation has the same form as the original Schroedinger equation in the region outside the range of the nuclear forces. The variables in this equation can be separated in a hyperspherical coordinate system and the resulting separate equations can be solved. Then using a superposition principle the solutions of the original equation are expanded in terms of solutions to the "equivalent" equation.
The Rayleigh-Ritz variational procedure is used to determine the coefficients of the expansions with a given potential. Because of the computational labor involved significant approximation is made in allowing only the leading terms in the angular variables to appear in the expansions while keeping a sufficient number of radial terms to insure convergence.
The present functions with a radial variable R = [formula omitted] give less than 1/2 of the binding energy predicted by Blatt, Derrick and Lyness (1962) who used a radial variable R = r₁₂ + r₂₃ + r₃₁. This shows that our approximation with the former radial variable is indeed too crude to predict a reliable value for the binding energy and that more angular terms must be included in the expansions, at least for the preponderent symmetric S-state.
Wave functions derived by the Rayleigh-Ritz variational principle are used to calculate cross sections for the reaction D(p, γ)He³. The electric dipole cross section depends very sensitively on the potential used to derive the wave function and a comparison with experimental data provides a test of the various model assumptions used to describe the nuclear interaction. A realistic potential must contain a tensor potential plus a hard core in the central potential. The tensor interaction couples the S and D states and is necessary to explain the quadrupole moment of He³ while the hard core produced the required mixed-symmetry S-state.
The experimentally observed isotropic component of the gamma ray yield is attributed to a magnetic dipole transition between a continuum quartet S-state and the mixed-symmetry component of the ground state wave function. For a range of the variable parameter used in the calculation comparison with experiment requires a 5% admixture of the mixed-symmetry S-state in the ground state wave function.
Subjects/Keywords: Helium – Isotopes; Three-body problem
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APA (6^{th} Edition):
Banville, M. R. (1965). A variational wave function for the ground state of He³, and its application to the D(p,y)He³ capture reaction. (Doctoral Dissertation). University of British Columbia. Retrieved from http://hdl.handle.net/2429/38375
Chicago Manual of Style (16^{th} Edition):
Banville, Marcel Roland. “A variational wave function for the ground state of He³, and its application to the D(p,y)He³ capture reaction.” 1965. Doctoral Dissertation, University of British Columbia. Accessed October 30, 2020.
http://hdl.handle.net/2429/38375.
MLA Handbook (7^{th} Edition):
Banville, Marcel Roland. “A variational wave function for the ground state of He³, and its application to the D(p,y)He³ capture reaction.” 1965. Web. 30 Oct 2020.
Vancouver:
Banville MR. A variational wave function for the ground state of He³, and its application to the D(p,y)He³ capture reaction. [Internet] [Doctoral dissertation]. University of British Columbia; 1965. [cited 2020 Oct 30].
Available from: http://hdl.handle.net/2429/38375.
Council of Science Editors:
Banville MR. A variational wave function for the ground state of He³, and its application to the D(p,y)He³ capture reaction. [Doctoral Dissertation]. University of British Columbia; 1965. Available from: http://hdl.handle.net/2429/38375
Purdue University
11.
Cox, Andrew D.
Transfers to a gravitational saddle point: An extended mission design option for LISA Pathfinder.
Degree: MSin Aeronautics and Astronautics, Aeronautics and Astronautics, 2016, Purdue University
URL: http://docs.lib.purdue.edu/open_access_theses/762
► Any possible LISA Pathfinder extended mission will immediately follow the primary mission after completion of scientific observations and technical demonstrations in a Sun-Earth L1…
(more)
▼ Any possible LISA Pathfinder extended mission will immediately follow the primary mission after completion of scientific observations and technical demonstrations in a Sun-Earth
L1 libration point orbit. One extended mission concept with scientific appeal is a spacecraft path that includes multiple encounters with a gravitational equilibrium point. This point, also termed a
saddle point, exists where the total gravitational acceleration sums to zero and is distinct from the five Lagrange points in the
three-
body problem. This investigation seeks a strategy to design such a path
subject to a variety of constraints. Periodic, quasi-periodic, and manifold structures are explored to supply useful transit behavior as well as arcs that repeatedly encounter the saddle point. A selection of these structures from the Earth-Moon and Sun-Earth circular restricted
three-
body problems are linked together via Poincaré mapping techniques and corrected in a higher-fidelity Sun-Earth-Moon bicircular restricted four-
body problem (BC4BP) and in an ephemeris environment. Additionally, natural motion in the BC4BP is leveraged to achieve the required encounters, and is similarly corrected to meet mission constraints. Results from both methods are detailed and compared to the mission requirements.
Advisors/Committee Members: Kathleen C. Howell, Kathleen C. Howell, William A. Crossley, Carolin E. Frueh.
Subjects/Keywords: Applied sciences; Bicircular restricted four-body problem; Circular restricted three-body problem; Design; LISA Pathfinder; Space; Trajectory; Aerospace Engineering
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APA (6^{th} Edition):
Cox, A. D. (2016). Transfers to a gravitational saddle point: An extended mission design option for LISA Pathfinder. (Thesis). Purdue University. Retrieved from http://docs.lib.purdue.edu/open_access_theses/762
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16^{th} Edition):
Cox, Andrew D. “Transfers to a gravitational saddle point: An extended mission design option for LISA Pathfinder.” 2016. Thesis, Purdue University. Accessed October 30, 2020.
http://docs.lib.purdue.edu/open_access_theses/762.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7^{th} Edition):
Cox, Andrew D. “Transfers to a gravitational saddle point: An extended mission design option for LISA Pathfinder.” 2016. Web. 30 Oct 2020.
Vancouver:
Cox AD. Transfers to a gravitational saddle point: An extended mission design option for LISA Pathfinder. [Internet] [Thesis]. Purdue University; 2016. [cited 2020 Oct 30].
Available from: http://docs.lib.purdue.edu/open_access_theses/762.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Cox AD. Transfers to a gravitational saddle point: An extended mission design option for LISA Pathfinder. [Thesis]. Purdue University; 2016. Available from: http://docs.lib.purdue.edu/open_access_theses/762
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Delft University of Technology
12.
Bonasera, Stefano (author).
On lunar collision orbits: New methodologies for Moon-to-Moon transfer design.
Degree: 2017, Delft University of Technology
URL: http://resolver.tudelft.nl/uuid:3df3ef2f-efcc-429d-b204-e0cbba196ef5
► Many interplanetary missions massively leverage the lunar gravitational pull in the so-called low-energy regime to converge to their aim, saving consistent amount of fuel. Among…
(more)
▼ Many interplanetary missions massively leverage the lunar gravitational pull in the so-called low-energy regime to converge to their aim, saving consistent amount of fuel. Among these, two future Japanese spacecraft are expected to repeatedly encounter the Moon along their trajectories to either facilitate the escape from the Earth–Moon system or opportunely target a speciﬁc region in its neighbourhood. Although never actively employed for preliminary trajectory design, lunar collision orbits have shown a rich dynamical structure and an applicability for both medium- and low-energy regimes. These characteristics, together with their intrinsic nature of being close to trajectories experiencing lunar ﬂy-by, have encouraged this research. In this work, lunar collision orbits are employed to delineate a method for obtaining ballistic transfers between two successive lunar encounters, brieﬂy addressed as Moon-to-Moon. This study is ﬁrst carried out with the assumptions of the autonomous Circular Restricted
Three-
Body Problem, subsequently extended to the nonautonomous Bi-circular Restricted Four-
Body Problem, including the solar gravitational inﬂuence. Poincaré cuts are extensively used as a dimensionality reductant for lunar collision orbits: this allows to ascertain their similar behaviour with trajectories ﬂybying the Moon, whose characteristics are partly foreseen by determining the associated intersection with the same cut. A patching is performed at the cut to obtain both single and multiple ballistic Moon-to-Moon transfers. The strict bond of lunar collision orbits with the invariant manifolds of simple periodic orbits about Lagrangian points is conﬁrmed and exploited to design ballistic itineraries connecting highly elliptic orbits about the Earth to horizontal Lyapunov orbits of the Earth–Moon system, via a single Moon-to-Moon transfer. With the usage of the lunar collision orbits and the Poincaré cut, a simple optimization technique is implemented to retrieve a properly deﬁned Moon-to-Moon transfer from a trajectory missing a second ﬂy-by with the Moon. Including the presence of the Sun, a similar method for obtaining single and multiple Moon-to-Moon transfers is developed. A classiﬁcation of lunar double-collision transfers is then performed within the same framework, highlighting their similarity with other studies in past literature, eventually leading to the construction of a database of Moon-to-Moon transfers. The latter, conceived as an improvement with respect to the former version by adding the lunar gravitational inﬂuence, shows its applicability in real preliminary trajectory design.
Advisors/Committee Members: Topputo, Francesco (mentor), Kawakatsu, Yasuhiro (mentor), Delft University of Technology (degree granting institution).
Subjects/Keywords: Moon-to-Moon transfer; Circular restricted three-body problem; Bicircular restricted four-body problem; Collision orbits; Levi Civita regularization; Poincaré map
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APA (6^{th} Edition):
Bonasera, S. (. (2017). On lunar collision orbits: New methodologies for Moon-to-Moon transfer design. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:3df3ef2f-efcc-429d-b204-e0cbba196ef5
Chicago Manual of Style (16^{th} Edition):
Bonasera, Stefano (author). “On lunar collision orbits: New methodologies for Moon-to-Moon transfer design.” 2017. Masters Thesis, Delft University of Technology. Accessed October 30, 2020.
http://resolver.tudelft.nl/uuid:3df3ef2f-efcc-429d-b204-e0cbba196ef5.
MLA Handbook (7^{th} Edition):
Bonasera, Stefano (author). “On lunar collision orbits: New methodologies for Moon-to-Moon transfer design.” 2017. Web. 30 Oct 2020.
Vancouver:
Bonasera S(. On lunar collision orbits: New methodologies for Moon-to-Moon transfer design. [Internet] [Masters thesis]. Delft University of Technology; 2017. [cited 2020 Oct 30].
Available from: http://resolver.tudelft.nl/uuid:3df3ef2f-efcc-429d-b204-e0cbba196ef5.
Council of Science Editors:
Bonasera S(. On lunar collision orbits: New methodologies for Moon-to-Moon transfer design. [Masters Thesis]. Delft University of Technology; 2017. Available from: http://resolver.tudelft.nl/uuid:3df3ef2f-efcc-429d-b204-e0cbba196ef5
Brno University of Technology
13.
Bahník, Michal.
Základy pohybu vesmírných těles: Basics of space motion.
Degree: 2019, Brno University of Technology
URL: http://hdl.handle.net/11012/26440
► This Bachelor thesis is a summarising text which deals with the issue of space motion. We analyse one-body, two-body and three-body problems. We derive analytical…
(more)
▼ This Bachelor thesis is a summarising text which deals with the issue of space motion. We analyse one-
body, two-
body and
three-
body problems. We derive analytical solution for the first two problems, from which we derive Kepler's laws, which are important for understanding of the space motion. We also discuss the relation of analytical solution to escape velocities. The closed form of analytical solution for general case of
three-
body problem does not exist. There are special cases, so-called stable orbits, for which the analytical solution is known. We design the numerical solution by explicit Runge-Kutta-Bogacki-Shampine method and back diferentiation method and we will test the results on the stable orbits.
Advisors/Committee Members: Kisela, Tomáš (advisor), Rozehnalová, Petra (referee).
Subjects/Keywords: Pohyb vesmírných těles; Kepler; probém dvou těles; problém tří těles; Space motion; Kepler; two-body problem; three-body problem
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APA ·
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APA (6^{th} Edition):
Bahník, M. (2019). Základy pohybu vesmírných těles: Basics of space motion. (Thesis). Brno University of Technology. Retrieved from http://hdl.handle.net/11012/26440
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16^{th} Edition):
Bahník, Michal. “Základy pohybu vesmírných těles: Basics of space motion.” 2019. Thesis, Brno University of Technology. Accessed October 30, 2020.
http://hdl.handle.net/11012/26440.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7^{th} Edition):
Bahník, Michal. “Základy pohybu vesmírných těles: Basics of space motion.” 2019. Web. 30 Oct 2020.
Vancouver:
Bahník M. Základy pohybu vesmírných těles: Basics of space motion. [Internet] [Thesis]. Brno University of Technology; 2019. [cited 2020 Oct 30].
Available from: http://hdl.handle.net/11012/26440.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Bahník M. Základy pohybu vesmírných těles: Basics of space motion. [Thesis]. Brno University of Technology; 2019. Available from: http://hdl.handle.net/11012/26440
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
14.
Suryawanshi, Jay Shriram.
Periodic Orbit Analytic Construction In The Circular Restricted Three-Body Problem.
Degree: MS, Mechanical & Aerospace Engineering, 2019, Old Dominion University
URL: 9781687972897
;
https://digitalcommons.odu.edu/mae_etds/300
► This thesis investigates an approximate analytic construction of halo-type periodic orbits about the collinear equilibrium points in the circular restricted three-body problem. The research…
(more)
▼ This thesis investigates an approximate analytic construction of halo-type periodic orbits about the collinear equilibrium points in the circular restricted
three-
body problem. The research follows a parallel approach to the one used by Ghazy and Newman, but the initial assumptions and utilized functions are unique to this thesis. A suppositional base solution constructed using Jacobi elliptic functions and satisfying Jacobi's integral equation is at the core of the analytic construction framework. The locus of this solution is a circle lying in the plane perpendicular to the line joining the primaries. The base solution elicits a closed-form expression for the period in terms of the elliptic integral of the first kind and a frequency-like parameter. The base solution satisfies a combination of third
body equations of motion in the y and z axes, and the equation of motion in the x axis is satisfied in an averaged and bounded sense when the vertical plane is located at one of the collinear Lagrange points.
Because the third
body cannot traverse this type of path naturally, an analytic correction process is pursued to recover accuracy. An iterated perturbation process is used whereby corrections to the base solution along the axis connecting the primaries is considered first, followed by correction in the other two directions. The iterated approach is followed to exploit the coupling structure inherent in the
three-
body system to simplify calculations. Linear assumptions are also used in these calculations for simplifying reasons. The non-homogeneous solution excitations for the x and y corrections are in the form of Fourier series expansions of the Jacobi elliptic functions in terms of the nome function. The development assumes the suppositional plane passes through one of the collinear Lagrange points. Only homogeneous correction is needed for the z axis. The modified solution then consists of the base solution plus first order corrections which can be further developed to include second and higher order corrections.
The base solution is compared with a L
_{1} halo orbit example and somewhat rough similarity is observed; the period of the base solution being approximately half of the true orbit. An interesting result is obtained when the truncated version of the correction forcing signal is compared with the exact one. When the frequency-like parameter is greater than or equal to unity, the full and truncated forcing signals become almost identical which justifies the use of the truncated forcing function for the L
_{1} halo orbit test case. The initial conditions for the true orbit are substituted in the truncated series solution and a new value of the frequency-like parameter is obtained using numerical computation depending in which axis is sought. For the test case, a unique value of the parameter is obtained from the y axis velocity initial conditions, which when employed in the x, y, and z solutions gives improved motion compared to the base one, and the corrected orbit reaches…
Advisors/Committee Members: Brett Newman, Colin Britcher, Gordon Melrose.
Subjects/Keywords: Analytic construction; Halo-type periodic orbits; Collinear equilibrium; Three-body problem; Aerospace Engineering
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APA ·
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APA (6^{th} Edition):
Suryawanshi, J. S. (2019). Periodic Orbit Analytic Construction In The Circular Restricted Three-Body Problem. (Thesis). Old Dominion University. Retrieved from 9781687972897 ; https://digitalcommons.odu.edu/mae_etds/300
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16^{th} Edition):
Suryawanshi, Jay Shriram. “Periodic Orbit Analytic Construction In The Circular Restricted Three-Body Problem.” 2019. Thesis, Old Dominion University. Accessed October 30, 2020.
9781687972897 ; https://digitalcommons.odu.edu/mae_etds/300.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7^{th} Edition):
Suryawanshi, Jay Shriram. “Periodic Orbit Analytic Construction In The Circular Restricted Three-Body Problem.” 2019. Web. 30 Oct 2020.
Vancouver:
Suryawanshi JS. Periodic Orbit Analytic Construction In The Circular Restricted Three-Body Problem. [Internet] [Thesis]. Old Dominion University; 2019. [cited 2020 Oct 30].
Available from: 9781687972897 ; https://digitalcommons.odu.edu/mae_etds/300.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Suryawanshi JS. Periodic Orbit Analytic Construction In The Circular Restricted Three-Body Problem. [Thesis]. Old Dominion University; 2019. Available from: 9781687972897 ; https://digitalcommons.odu.edu/mae_etds/300
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Texas – Austin
15.
-9471-2196.
Exploration and optimization of low-energy capture options at Jovian moons.
Degree: PhD, Aerospace Engineering, 2018, University of Texas – Austin
URL: http://hdl.handle.net/2152/68928
► A key trade-off for planetary system exploration is the fuel cost required versus science data obtained. Historically, planetary systems have been explored utilizing multiple flybys,…
(more)
▼ A key trade-off for planetary system exploration is the fuel cost required versus science data obtained. Historically, planetary systems have been explored utilizing multiple flybys, such as Galileo, Cassini's complex Saturnian tour, as well as the trajectory for the proposed Europa Clipper mission. While this approach eliminates the need for expensive capture maneuvers, it can require days to weeks between observations, limiting available science data. An alternative that seeks to maximize science return is to capture about each moon of interest. Investigations of low-energy dynamics have shown the existence of relatively inexpensive transfers between halo orbits at different moons. Chaining these transfers in a moon-hopping tour allows one spacecraft to visit multiple moons. The next step for a multi-moon mission is to connect the inter-moon transfers to science orbits at specific moons. Two capture orbit scenarios are considered for comparison: 1) traditional, tightly captured low-altitude orbits and 2) low-energy, loosely captured high-altitude orbits. Near-global grid search methods are developed to generate initial capture trajectories from staging halo orbits. To help determine which solutions are near optimal, an analytical expression for the predicted floor cost is derived. Low cost captures are identified and optimized using impulsive primer vector theory to determine the ideal number and location of impulses. The trajectory is then extended to include the last resonant-orbit of the inter-moon transfer, using the halo orbit as a patch point to connect the phases. A new
three-dimensional periodic orbit that naturally transfers between the resonant and halo orbits is generated to facilitate the connection. The resulting resonant-to-capture transfers are again optimized with primer vector theory, resulting in several optimized options for comparison. As an additional mission design option, the possibilities of advanced exploration using an electrodynamic tether are investigated. An approximation to the tether-perturbed dynamics is derived that allows for an integral of motion, enabling useful analytical techniques. New periodic orbit families are generated as a function of tether length, using continuation from non-perturbed Lyapunov orbits. The new orbits are analyzed in terms of stability and utility for future use in mission design.
Advisors/Committee Members: Russell, Ryan Paul, 1976- (advisor), Bettadpur, Srinivas V (committee member), Akella, Maruthi R (committee member), Jones, Brandon (committee member), Petropoulos, Anastassios E (committee member).
Subjects/Keywords: Low-energy dynamics; Periodic orbits; Capture; Europa; Primer vector; Three-body problem
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APA (6^{th} Edition):
-9471-2196. (2018). Exploration and optimization of low-energy capture options at Jovian moons. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/68928
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Chicago Manual of Style (16^{th} Edition):
-9471-2196. “Exploration and optimization of low-energy capture options at Jovian moons.” 2018. Doctoral Dissertation, University of Texas – Austin. Accessed October 30, 2020.
http://hdl.handle.net/2152/68928.
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
MLA Handbook (7^{th} Edition):
-9471-2196. “Exploration and optimization of low-energy capture options at Jovian moons.” 2018. Web. 30 Oct 2020.
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Vancouver:
-9471-2196. Exploration and optimization of low-energy capture options at Jovian moons. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2018. [cited 2020 Oct 30].
Available from: http://hdl.handle.net/2152/68928.
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Council of Science Editors:
-9471-2196. Exploration and optimization of low-energy capture options at Jovian moons. [Doctoral Dissertation]. University of Texas – Austin; 2018. Available from: http://hdl.handle.net/2152/68928
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Luleå University of Technology
16.
Celik, Onur.
ORBITAL ENVIRONMENT CONSIDERATIONS DURING THE CLOSE APPROACH PHASE OF MISSIONS TO SMALL BODIES.
Degree: 2016, Luleå University of Technology
URL: http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-47143
► Missions to small bodies have become increasingly attractive in recent years, firstly, due to their scientific value, but also because of their potential risk…
(more)
▼ Missions to small bodies have become increasingly attractive in recent years, firstly, due to their scientific value, but also because of their potential risk to Earth and prospective economic return. A variety of missions have been proposed, ranging from manned exploration to commercial mining missions. There have already been missions to asteroids (e.g. Hayabusa) which brought samples and scientific data, while successor spacecraft are on their way to new targets. For such and future missions, it is essential to perform in-situ observations by landers in order to enhance scientific return. Simple, reliable and low-cost lander modules would satisfy the desired observational capability by exploiting the natural dynamics of these bodies. Therefore, CubeSat systems are good candidates to fulfil the aforementioned exploration demands. This research considers a mission that is targeted to binary asteroid system, which constitute 15% of NEA population. The mission architecture includes a mothership carrying one or several CubeSats. CubeSat deployment is performed by a spring mechanism which is limited for maximum velocity. Natural landing trajectories are investigated after deployment for an unpowered CubeSat within the dynamics of binary system by using the frame of Circular Restricted Three Body Problem (CR3BP). Landing is envisaged in local vertical direction in order to avoid damage to the CubeSat. Dynamical model is propagated backwards from the surface in a novel bisection algorithm to obtain lowest energy trajectories. CR3BP only considers point mass gravity in the model, therefore a perturbation analysis is carried to find out when solar radiation pressure would dominate the evolution of trajectories. The research provides new insights into the regions and sizes of binary systems that could potentially be explored by a simple, underactuated lander with very little control. Suggestions are also made for a CubeSat that could possibly be employed as a lander for small body exploration.
Validerat; 20160317 (global_studentproject_submitter)
Subjects/Keywords: Technology; Small body exploration; Binary asteroids; Ballistic landing; Natural trajectories; CubeSat; The Circular Restricted Three Body Problem; Teknik
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APA (6^{th} Edition):
Celik, O. (2016). ORBITAL ENVIRONMENT CONSIDERATIONS DURING THE CLOSE APPROACH PHASE OF MISSIONS TO SMALL BODIES. (Thesis). Luleå University of Technology. Retrieved from http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-47143
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16^{th} Edition):
Celik, Onur. “ORBITAL ENVIRONMENT CONSIDERATIONS DURING THE CLOSE APPROACH PHASE OF MISSIONS TO SMALL BODIES.” 2016. Thesis, Luleå University of Technology. Accessed October 30, 2020.
http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-47143.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7^{th} Edition):
Celik, Onur. “ORBITAL ENVIRONMENT CONSIDERATIONS DURING THE CLOSE APPROACH PHASE OF MISSIONS TO SMALL BODIES.” 2016. Web. 30 Oct 2020.
Vancouver:
Celik O. ORBITAL ENVIRONMENT CONSIDERATIONS DURING THE CLOSE APPROACH PHASE OF MISSIONS TO SMALL BODIES. [Internet] [Thesis]. Luleå University of Technology; 2016. [cited 2020 Oct 30].
Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-47143.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Celik O. ORBITAL ENVIRONMENT CONSIDERATIONS DURING THE CLOSE APPROACH PHASE OF MISSIONS TO SMALL BODIES. [Thesis]. Luleå University of Technology; 2016. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-47143
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Purdue University
17.
Guzzetti, Davide.
Coupled orbit-attitude mission design in the circular restricted three-body problem.
Degree: PhD, Aeronautics and Astronautics, 2016, Purdue University
URL: https://docs.lib.purdue.edu/open_access_dissertations/657
► Trajectory design increasingly leverages multi-body dynamical structures that are based on an understanding of various types of orbits in the Circular Restricted Three-Body Problem…
(more)
▼ Trajectory design increasingly leverages multi-
body dynamical structures that are based on an understanding of various types of orbits in the Circular Restricted
Three-
Body Problem (CR3BP). Given the more complex dynamical environment, mission applications may also benefit from deeper insight into the attitude motion. In this investigation, the attitude dynamics are coupled with the trajectories in the CR3BP. In a highly sensitive dynamical model, such as the orbit-attitude CR3BP, periodic solutions allow delineation of the fundamental dynamical structures. Periodic solutions are also a subset of motions that are bounded over an infinite time-span (assuming no perturbing factors), without the necessity to integrate over an infinite time interval. Euler equations of motion and quaternion kinematics describe the rotational behavior of the spacecraft, whereas the translation of the center of mass is modeled in the CR3BP equations. A multiple shooting and continuation procedure are employed to target orbit-attitude periodic solutions in this model. Application of Floquet theory, Poincaré mapping, and grid search to identify initial guesses for the targeting algorithm is described. In the Earth-Moon system, representative scenarios are explored for axisymmetric vehicles with various inertia characteristics, assuming that the vehicles move along Lyapunov, halo as well as distant retrograde orbits. A rich structure of possible periodic behaviors appears to pervade the solution space in the coupled
problem. The stability analysis of the attitude dynamics for the selected families is included. Among the computed solutions, marginally stable and slowly diverging rotational behaviors exist and may offer interesting mission applications. Additionally, the solar radiation pressure is included and a fully coupled orbit-attitude model is developed. With specific application to solar sails, various guidance algorithms are explored to direct the spacecraft along a desired path, when the mutual interaction between orbit and attitude dynamics is considered. Each strategy implements a different form of control input, ranging from instantaneous reorientation of the sail pointing direction to the application of control torques, and it is demonstrated within a simple station keeping scenario.
Advisors/Committee Members: Kathleen C. Howell, Kathleen C. Howell, Michele R. Lavagna, James M. Longuski, Dengfeng Sun.
Subjects/Keywords: Applied sciences; Libration points; Multi-body systems; Periodic solutions; Solar sails; Spacecraft attitude; Three-body problem; Aerospace Engineering
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Manager
APA (6^{th} Edition):
Guzzetti, D. (2016). Coupled orbit-attitude mission design in the circular restricted three-body problem. (Doctoral Dissertation). Purdue University. Retrieved from https://docs.lib.purdue.edu/open_access_dissertations/657
Chicago Manual of Style (16^{th} Edition):
Guzzetti, Davide. “Coupled orbit-attitude mission design in the circular restricted three-body problem.” 2016. Doctoral Dissertation, Purdue University. Accessed October 30, 2020.
https://docs.lib.purdue.edu/open_access_dissertations/657.
MLA Handbook (7^{th} Edition):
Guzzetti, Davide. “Coupled orbit-attitude mission design in the circular restricted three-body problem.” 2016. Web. 30 Oct 2020.
Vancouver:
Guzzetti D. Coupled orbit-attitude mission design in the circular restricted three-body problem. [Internet] [Doctoral dissertation]. Purdue University; 2016. [cited 2020 Oct 30].
Available from: https://docs.lib.purdue.edu/open_access_dissertations/657.
Council of Science Editors:
Guzzetti D. Coupled orbit-attitude mission design in the circular restricted three-body problem. [Doctoral Dissertation]. Purdue University; 2016. Available from: https://docs.lib.purdue.edu/open_access_dissertations/657
18.
Alexandre Lacerda Machuy Francisco.
Estudo de trajetórias para veículos espacais utilizando captura gravitacional.
Degree: 2009, Instituto Nacional de Pesquisas Espaciais
URL: http://urlib.net/sid.inpe.br/[email protected]/2009/07.30.14.13
► Vindo de fora da esfera de influência gravitacional de um corpo celeste, um veículo espacial pode ter sua velocidade relativa a esse corpo reduzida ao…
(more)
▼ Vindo de fora da esfera de influência gravitacional de um corpo celeste, um veículo espacial pode ter sua velocidade relativa a esse corpo reduzida ao ponto de fazer com que esse veículo permaneça por algum tempo em órbita em torno desse corpo celeste. Este mecanismo é conhecido como captura gravitacional temporária. Neste trabalho foi feito o estudo numérico de captura gravitacional, usando como modelos matemáticos o problema de três corpos restrito circular e o problema bi circular de quatro corpos. Sempre comparamos os resultados obtidos nos dois modelos. Captura gravitacional tem varias aplicações praticas em uma missão espacial, como por exemplo a análise do consumo mínimo de combustível de uma transferência Terra-Lua.
Coming from outside the sphere of influence of a celestial body, a space vehicle can have its relative velocity with respect to that body reduced to the point where that vehicle stays for some time in orbit around that body. This mechanism is known as temporary gravitational capture. In this work, a numerical study of gravitational capture was performed, using as mathematical models the circular restricted problem of three bodies and the bicircular problem of four bodies. We always compared the results obtained in the two models. The gravitational capture has several practical applications in space missions. An example would be the analysis of the minimum consumption of fuel for an Earth-Moon transfer.
Advisors/Committee Members: Rodolpho Vilhena de Moraes, Antonio Fernando Bertachini de Almeida Prado, Terezinha de Jesus Stuchi, Mario Cesar Ricci, André Fenili, Carlos Renato Solorzano.
Subjects/Keywords: mecânica celeste; captura gravitacional; problema de três corpos; problema de quatro corpos; celestial mechanic; gravitacional capture; three body problem; four body problem
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APA (6^{th} Edition):
Francisco, A. L. M. (2009). Estudo de trajetórias para veículos espacais utilizando captura gravitacional. (Thesis). Instituto Nacional de Pesquisas Espaciais. Retrieved from http://urlib.net/sid.inpe.br/[email protected]/2009/07.30.14.13
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16^{th} Edition):
Francisco, Alexandre Lacerda Machuy. “Estudo de trajetórias para veículos espacais utilizando captura gravitacional.” 2009. Thesis, Instituto Nacional de Pesquisas Espaciais. Accessed October 30, 2020.
http://urlib.net/sid.inpe.br/[email protected]/2009/07.30.14.13.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7^{th} Edition):
Francisco, Alexandre Lacerda Machuy. “Estudo de trajetórias para veículos espacais utilizando captura gravitacional.” 2009. Web. 30 Oct 2020.
Vancouver:
Francisco ALM. Estudo de trajetórias para veículos espacais utilizando captura gravitacional. [Internet] [Thesis]. Instituto Nacional de Pesquisas Espaciais; 2009. [cited 2020 Oct 30].
Available from: http://urlib.net/sid.inpe.br/[email protected]/2009/07.30.14.13.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Francisco ALM. Estudo de trajetórias para veículos espacais utilizando captura gravitacional. [Thesis]. Instituto Nacional de Pesquisas Espaciais; 2009. Available from: http://urlib.net/sid.inpe.br/[email protected]/2009/07.30.14.13
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
19.
Κόλλιας, Νικόλαος.
Μελέτη οικογενειών περιοδικών λύσεων γύρω από τα τριγωνικά σημεία ισορροπίας στο φωτοβαρυτικό πρόβλημα των τριών σωμάτων.
Degree: 2008, University of Patras
URL: http://nemertes.lis.upatras.gr/jspui/handle/10889/1074
► Αντικείμενο της παρούσης διπλωματικής εργασίας αποτελεί το Φωτοβαρυτικό Πρόβλημα των Τριών Σωμάτων, ένα άλυτο πρόβλημα που απασχόλησε και εξακολουθεί να απασχολεί τον τομέα των Εφαρμοσμένων…
(more)
▼ Αντικείμενο της παρούσης διπλωματικής εργασίας αποτελεί το Φωτοβαρυτικό Πρόβλημα των Τριών Σωμάτων, ένα άλυτο πρόβλημα που απασχόλησε και εξακολουθεί να απασχολεί τον τομέα των Εφαρμοσμένων Μαθηματικών και της Κλασικής Αστροφυσικής τουλάχιστον τους τελευταίους δύο αιώνες. Διεξάγεται μελέτη των σημείων ισορροπίας του συστήματος και προσδιορίζονται οικογένειες περιοδικών λύσεων, οι οποίες στην περίπτωσή μας διακρίνονται σε δύο κατηγορίες που χαρακτηρίζονται από το μέγεθος της περιόδου τους.
The topic of this thesis deals with the Restricted Photogravitational Three Body Problem, which is an unsolved problem in Astrophysics and Celestial Mechanics. Research is carried out concerning the equilibrium points, around which families of periodic solutions can be identified.
Advisors/Committee Members: Ράγγος, Όμηρος, Kollias, Nick, Ράγγος, Όμηρος, Ζαγούρας, Χαράλαμπος, Περδίος, Ευστάθιος.
Subjects/Keywords: Φωτοβαρυτικό πρόβλημα των τριών σωμάτων; Τριγωνικά σημεία ισορροπίας; 521; Photogravitational three body problem; Triangular equilibrium points
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APA (6^{th} Edition):
Κόλλιας, . (2008). Μελέτη οικογενειών περιοδικών λύσεων γύρω από τα τριγωνικά σημεία ισορροπίας στο φωτοβαρυτικό πρόβλημα των τριών σωμάτων. (Masters Thesis). University of Patras. Retrieved from http://nemertes.lis.upatras.gr/jspui/handle/10889/1074
Chicago Manual of Style (16^{th} Edition):
Κόλλιας, Νικόλαος. “Μελέτη οικογενειών περιοδικών λύσεων γύρω από τα τριγωνικά σημεία ισορροπίας στο φωτοβαρυτικό πρόβλημα των τριών σωμάτων.” 2008. Masters Thesis, University of Patras. Accessed October 30, 2020.
http://nemertes.lis.upatras.gr/jspui/handle/10889/1074.
MLA Handbook (7^{th} Edition):
Κόλλιας, Νικόλαος. “Μελέτη οικογενειών περιοδικών λύσεων γύρω από τα τριγωνικά σημεία ισορροπίας στο φωτοβαρυτικό πρόβλημα των τριών σωμάτων.” 2008. Web. 30 Oct 2020.
Vancouver:
Κόλλιας . Μελέτη οικογενειών περιοδικών λύσεων γύρω από τα τριγωνικά σημεία ισορροπίας στο φωτοβαρυτικό πρόβλημα των τριών σωμάτων. [Internet] [Masters thesis]. University of Patras; 2008. [cited 2020 Oct 30].
Available from: http://nemertes.lis.upatras.gr/jspui/handle/10889/1074.
Council of Science Editors:
Κόλλιας . Μελέτη οικογενειών περιοδικών λύσεων γύρω από τα τριγωνικά σημεία ισορροπίας στο φωτοβαρυτικό πρόβλημα των τριών σωμάτων. [Masters Thesis]. University of Patras; 2008. Available from: http://nemertes.lis.upatras.gr/jspui/handle/10889/1074
Penn State University
20.
Scott, Christopher James.
Transfer and Capture into Distant Retrograde Orbits
.
Degree: 2010, Penn State University
URL: https://submit-etda.libraries.psu.edu/catalog/10471
► This dissertation utilizes theory and techniques derived from the fields of dynamical systems theory, astrodyanamics, celestial mechanics, and fluid mechanics to analyze the phenomenon of…
(more)
▼ This dissertation utilizes theory and techniques derived from the fields of dynamical systems theory, astrodyanamics, celestial mechanics, and fluid mechanics to analyze the phenomenon of satellite capture and interrelated spacecraft transfers in restricted
three-
body systems. The results extend current knowledge and understanding of capture dynamics in the context of astrodynamics and celestial mechanics.
Manifold theory, fast Lyapunov indicator maps, and the classification of space structure facilitate an analysis of the transport of objects from the chaotic reaches of the solar system to the distant retrograde region in the sun-Jupiter system. Apart from past studies this dissertation considers the role of the complex lobe structure encompassing stable regions in the circular restricted
three-
body problem. These structures are shown to be responsible for the phenomenon of sticky orbits and the transport of objects among stable regions. Since permanent capture can only be achieved through a change in energy, fast Lyapunov indicator maps and other methods which reveal the structure of the conservative system are used to discern capture regions and identify the underpinnings of the dynamics. Fast Lyapunov indicator maps provide an accurate classification of orbits of permanent capture and escape, yet monopolize computational resources. In anticipation of a fully
three-dimensional analysis in the dissipative system a new mapping parameter is introduced based on energy degradation and averaged velocity. Although the study specifically addresses the sun-Jupiter system, the qualitative results and devised techniques can be applied throughout the solar system and to capture about extrasolar planets.
Extending the analysis beyond the exterior of the stable distant retrograde region fosters the construction of transfer orbits from low-Earth orbit to a stable periodic orbit at the center of the stable distant retrograde region. Key to this analysis is the predictability of collision orbits within the highly chaotic region commonly recognized as a saddle point on the energy manifold. The pragmatic techniques derived from this analysis solve a number of complications apparent in the literature. Notably a reliable methodology for the construction of an arbitrary number of transfer orbits circumvents the requirement of computing specialized periodic orbits or extensive numerical sampling of the phase space. The procedure provides a complete description of the design space accessing a wide range of distant retrograde orbits sizes, insertion points, and parking orbit altitudes in an automated manner. The transfers are studied in a similar fashion to periodic orbits unveiling the intimate relationship among design parameters and phase space structure. An arbitrary number of Earth return periodic orbits can be generated as a by-product. These orbits may be useful for spacecraft that must make a number of passes near the second primary without a reduction in energy.
Further analysis of the lobe dynamics and a…
Advisors/Committee Members: Dr David B Spencer, Dissertation Advisor/Co-Advisor, David Bradley Spencer, Committee Chair/Co-Chair, Robert Graham Melton, Committee Member, Jack W Langelaan, Committee Member, Joseph Paul Cusumano, Committee Member.
Subjects/Keywords: circular restricted three body problem; Astrodynamics; CR3BP; satellite capture
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APA (6^{th} Edition):
Scott, C. J. (2010). Transfer and Capture into Distant Retrograde Orbits
. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/10471
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16^{th} Edition):
Scott, Christopher James. “Transfer and Capture into Distant Retrograde Orbits
.” 2010. Thesis, Penn State University. Accessed October 30, 2020.
https://submit-etda.libraries.psu.edu/catalog/10471.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7^{th} Edition):
Scott, Christopher James. “Transfer and Capture into Distant Retrograde Orbits
.” 2010. Web. 30 Oct 2020.
Vancouver:
Scott CJ. Transfer and Capture into Distant Retrograde Orbits
. [Internet] [Thesis]. Penn State University; 2010. [cited 2020 Oct 30].
Available from: https://submit-etda.libraries.psu.edu/catalog/10471.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Scott CJ. Transfer and Capture into Distant Retrograde Orbits
. [Thesis]. Penn State University; 2010. Available from: https://submit-etda.libraries.psu.edu/catalog/10471
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Penn State University
21.
Nayyar, Mollik.
Optimal Earth Return Transfers from Lagrange Point Orbits Using Particle Swarm Optimization.
Degree: 2016, Penn State University
URL: https://submit-etda.libraries.psu.edu/catalog/12617mxn244
► A future where space mining and cargo transportation is fast approaching reality, for such a future, one needs a way to efficiently transport the materials…
(more)
▼ A future where space mining and cargo transportation is fast approaching reality, for such a future, one needs a way to efficiently transport the materials gathered in space to Earth or other space based depots. The focus of this thesis is on such return trajectories from Lagrange point orbits to Earth. Since travel in space is currently very expensive, it is desired to utilize more efficient methods to travel through space. Current trajectory design methods require a lot of computational resource which contributes to mission cost. This thesis presents an approximate, computationally inexpensive method to scan the available search space and obtain the locations and trajectories associated the with lowest ΔV, which can be used as an initial guess that can be later used in advanced methods to obtain ΔV optimal trajectories. The use of invariant manifolds in the Earth-Moon system is proposed for this purpose. The
three-
body system is studied and a simplified methodology for the design of trajectories from the Lagrange point orbits is presented. The techniques to generate the invariant manifold associated with Lagrange point orbits is presented. To obtain the best possible trajectory based on ΔV requirements, an optimization scheme is introduced to select the best location on the manifold to initiate transfer. While gradient based methods have been previously used to study optimal trajectories in the
three-
body system, these are computationally very expensive. Therefore, this thesis tackles the computational requirements associated with design of the space trajectories in the Earth-Moon-spacecraft
three-
body system for space transportation. The solver used to survey the search space of the invariant manifold is presented. The two-
body approximation is utilized to provide quick, preliminary study of the transfers in space, allowing the mission designer to be able to devise a suitable trajectory in the
three-
body system using the insights from the two-
body approximation. Essentially, the burden of finding the location of the transfer point with the minimum ΔV transfer is offloaded to the particle swarm optimization algorithm that uses a simplified Lambert's solver to scan the search space on the manifold and provide the patch point with the lowest ΔV. The solver used here is validated using the results obtained from literature for transfers from Earth to a Lagrange point orbit. Validation results show that the technique used is able to provide fairly accurate results for a two-impulse scenario at a very significant computational advantage. Then, the method is used to generate results for Earth return trajectories. The ΔV requirements from Lambert's solver for halo and Lyapunov orbits of L_1,L_2 points are presented. The trends obtained using this method shows the location of orbit insertion in the LEO that has the potential of providing the lowest ΔV. The present analysis suggests that it is possible to reach almost any inclination from the manifold of a halo LPO without incurring huge ΔV costs if the target location for…
Advisors/Committee Members: Dr David Spencer, Thesis Advisor/Co-Advisor.
Subjects/Keywords: Three body system; Lagrange points; manifolds; optimization; particle swarm; PSO; Dynamical Systems; Optimal Transfers; Astrodynamics; Lagrange Point Orbits; LPO; Lambert's Problem
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APA ·
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APA (6^{th} Edition):
Nayyar, M. (2016). Optimal Earth Return Transfers from Lagrange Point Orbits Using Particle Swarm Optimization. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/12617mxn244
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16^{th} Edition):
Nayyar, Mollik. “Optimal Earth Return Transfers from Lagrange Point Orbits Using Particle Swarm Optimization.” 2016. Thesis, Penn State University. Accessed October 30, 2020.
https://submit-etda.libraries.psu.edu/catalog/12617mxn244.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7^{th} Edition):
Nayyar, Mollik. “Optimal Earth Return Transfers from Lagrange Point Orbits Using Particle Swarm Optimization.” 2016. Web. 30 Oct 2020.
Vancouver:
Nayyar M. Optimal Earth Return Transfers from Lagrange Point Orbits Using Particle Swarm Optimization. [Internet] [Thesis]. Penn State University; 2016. [cited 2020 Oct 30].
Available from: https://submit-etda.libraries.psu.edu/catalog/12617mxn244.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Nayyar M. Optimal Earth Return Transfers from Lagrange Point Orbits Using Particle Swarm Optimization. [Thesis]. Penn State University; 2016. Available from: https://submit-etda.libraries.psu.edu/catalog/12617mxn244
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
22.
Ζαγούρας, Χαράλαμπος Γ.
Δευτέρας και τρίτης τάξεως μεταβολαί εις το περιορισμένον πρόβλημα των τριών σωμάτων.
Degree: 1973, University of Patras
URL: http://nemertes.lis.upatras.gr/jspui/handle/10889/3578
Subjects/Keywords: Πρόβλημα των τριών σωμάτων; 515.352; Three body problem
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APA (6^{th} Edition):
Ζαγούρας, . . (1973). Δευτέρας και τρίτης τάξεως μεταβολαί εις το περιορισμένον πρόβλημα των τριών σωμάτων. (Doctoral Dissertation). University of Patras. Retrieved from http://nemertes.lis.upatras.gr/jspui/handle/10889/3578
Chicago Manual of Style (16^{th} Edition):
Ζαγούρας, Χαράλαμπος Γ. “Δευτέρας και τρίτης τάξεως μεταβολαί εις το περιορισμένον πρόβλημα των τριών σωμάτων.” 1973. Doctoral Dissertation, University of Patras. Accessed October 30, 2020.
http://nemertes.lis.upatras.gr/jspui/handle/10889/3578.
MLA Handbook (7^{th} Edition):
Ζαγούρας, Χαράλαμπος Γ. “Δευτέρας και τρίτης τάξεως μεταβολαί εις το περιορισμένον πρόβλημα των τριών σωμάτων.” 1973. Web. 30 Oct 2020.
Vancouver:
Ζαγούρας . Δευτέρας και τρίτης τάξεως μεταβολαί εις το περιορισμένον πρόβλημα των τριών σωμάτων. [Internet] [Doctoral dissertation]. University of Patras; 1973. [cited 2020 Oct 30].
Available from: http://nemertes.lis.upatras.gr/jspui/handle/10889/3578.
Council of Science Editors:
Ζαγούρας . Δευτέρας και τρίτης τάξεως μεταβολαί εις το περιορισμένον πρόβλημα των τριών σωμάτων. [Doctoral Dissertation]. University of Patras; 1973. Available from: http://nemertes.lis.upatras.gr/jspui/handle/10889/3578
23.
Παπαϊώννου, Απόστολος Ι.
Επτά νέαι οικογένειαι τριδιάστατων περιοδικών λύσεων διπλής συμμετρίας του περιωρισμένου προβλήματος των τριών σωμάτων.
Degree: 1974, University of Patras
URL: http://nemertes.lis.upatras.gr/jspui/handle/10889/3801
Subjects/Keywords: Πρόβλημα των τριών σωμάτων; 515.352; Three body problem
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APA (6^{th} Edition):
Παπαϊώννου, . . (1974). Επτά νέαι οικογένειαι τριδιάστατων περιοδικών λύσεων διπλής συμμετρίας του περιωρισμένου προβλήματος των τριών σωμάτων. (Doctoral Dissertation). University of Patras. Retrieved from http://nemertes.lis.upatras.gr/jspui/handle/10889/3801
Chicago Manual of Style (16^{th} Edition):
Παπαϊώννου, Απόστολος Ι. “Επτά νέαι οικογένειαι τριδιάστατων περιοδικών λύσεων διπλής συμμετρίας του περιωρισμένου προβλήματος των τριών σωμάτων.” 1974. Doctoral Dissertation, University of Patras. Accessed October 30, 2020.
http://nemertes.lis.upatras.gr/jspui/handle/10889/3801.
MLA Handbook (7^{th} Edition):
Παπαϊώννου, Απόστολος Ι. “Επτά νέαι οικογένειαι τριδιάστατων περιοδικών λύσεων διπλής συμμετρίας του περιωρισμένου προβλήματος των τριών σωμάτων.” 1974. Web. 30 Oct 2020.
Vancouver:
Παπαϊώννου . Επτά νέαι οικογένειαι τριδιάστατων περιοδικών λύσεων διπλής συμμετρίας του περιωρισμένου προβλήματος των τριών σωμάτων. [Internet] [Doctoral dissertation]. University of Patras; 1974. [cited 2020 Oct 30].
Available from: http://nemertes.lis.upatras.gr/jspui/handle/10889/3801.
Council of Science Editors:
Παπαϊώννου . Επτά νέαι οικογένειαι τριδιάστατων περιοδικών λύσεων διπλής συμμετρίας του περιωρισμένου προβλήματος των τριών σωμάτων. [Doctoral Dissertation]. University of Patras; 1974. Available from: http://nemertes.lis.upatras.gr/jspui/handle/10889/3801
University of Surrey
24.
Gonul, Bulent.
Extended adiabatic treatments of continuum channels in nuclear stripping pickup reactions.
Degree: PhD, 1994, University of Surrey
URL: http://epubs.surrey.ac.uk/844378/
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.308410
► Although the quasi-adiabatic calculations have led to an improved description of the measured observables, the theoretical justifications of the assumptions made in the model have…
(more)
▼ Although the quasi-adiabatic calculations have led to an improved description of the measured observables, the theoretical justifications of the assumptions made in the model have not yet been studied. The first part of the work described in this thesis is therefore concerned with the clarification of these theoretical uncertainties by performing a rigorous investigation of the accuracy and the validity of the model. In addition, we reformulate the quasi-adiabatic theory to give a more general formalism, approaching the three-body problem in a different way. This alternative formulation provides a clear understanding of the assumptions made in the original quasi-adiabatic theory. Using the spirit of the new quasi-adiabatic formalism, we also develop alternative approximation schemes for the treatment of quantum mechanical three-body systems. The accuracy and the range of validity of the developments, together with the quasi-adiabatic theory, are investigated carefully and precisely by comparing their predictions with those essentially exact CDCC technique for the 66Zn (d,p)67Zn reaction at 88.2 MeV. It is found that the alternative models and quasi-adiabatic theory are reliable techniques for the treatment of deuteron breakup process at intermediate energies of interest. The remainder of this thesis is devoted to the investigation of the mechanism of (p,d*) reactions. As the treatment of the final state interactions in such reactions has not previously been studied consistently, we develop an adiabatic method and apply it to new data for the 13C(p,d)12C reaction with 35 MeV incident proton energy. Due to the weak coupling between spin channels of the continuum n-p system at the energies of interest, the singlet and triplet state pickup cross-sections for the final n-p system are analyzed separately. We find that the contribution from the singlet state is dominant for small relative energies while the triplet state dominates for large energies. This application clarifies the relationship between the three-body dynamics in the final state of (p,d) and (p,d*) reactions.
Subjects/Keywords: 530.1; Quasi-adiabatic theory; Three-body problem
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APA (6^{th} Edition):
Gonul, B. (1994). Extended adiabatic treatments of continuum channels in nuclear stripping pickup reactions. (Doctoral Dissertation). University of Surrey. Retrieved from http://epubs.surrey.ac.uk/844378/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.308410
Chicago Manual of Style (16^{th} Edition):
Gonul, Bulent. “Extended adiabatic treatments of continuum channels in nuclear stripping pickup reactions.” 1994. Doctoral Dissertation, University of Surrey. Accessed October 30, 2020.
http://epubs.surrey.ac.uk/844378/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.308410.
MLA Handbook (7^{th} Edition):
Gonul, Bulent. “Extended adiabatic treatments of continuum channels in nuclear stripping pickup reactions.” 1994. Web. 30 Oct 2020.
Vancouver:
Gonul B. Extended adiabatic treatments of continuum channels in nuclear stripping pickup reactions. [Internet] [Doctoral dissertation]. University of Surrey; 1994. [cited 2020 Oct 30].
Available from: http://epubs.surrey.ac.uk/844378/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.308410.
Council of Science Editors:
Gonul B. Extended adiabatic treatments of continuum channels in nuclear stripping pickup reactions. [Doctoral Dissertation]. University of Surrey; 1994. Available from: http://epubs.surrey.ac.uk/844378/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.308410
Hong Kong University of Science and Technology
25.
Chi, Xuguang.
A non-variational approach to the quantum three-body coulomb problem.
Degree: 2004, Hong Kong University of Science and Technology
URL: http://repository.ust.hk/ir/Record/1783.1-2356
;
https://doi.org/10.14711/thesis-b849116
;
http://repository.ust.hk/ir/bitstream/1783.1-2356/1/th_redirect.html
► This thesis presents a general non-variational approach to the solution of three-body Schrödinger's equation with Coulomb interactions, based on the utilization of symmetries intrinsic to…
(more)
▼ This thesis presents a general non-variational approach to the solution of three-body Schrödinger's equation with Coulomb interactions, based on the utilization of symmetries intrinsic to the three-body Laplacian operator first proposed by W.Y.Hsiang. Through step by step reductions, the center of mass degree of freedom is first removed, followed by the separation of all the rotational degrees of freedom, leading to a coupled partial differential equations (PDEs) in terms of the rotationally invariant internal variables {f1, f2, f3}. A crucial observation is that in the subspace where all the rotational degrees of freedom have been removed, there is an intrinsic spherical symmetry which can be fully utilized through the introduction of hyperspherical coordinates. By expressing the reduced Schrödinger's PDEs (with all the rotational degrees of freedom separated out) in terms of the hyperspherical coordinates, with the subsequent introduction of Jacobi polynomials as the angular eigenfunctions and Laguerre polynomials to expand the radial component, a system of infinite linear algebraic equations is obtained for the expansion coefficients. A numerical scheme is presented whereby the Coulomb interaction matrix elements are calculated to a very high degree of accuracy with minimal effort, and the truncation of the linear equations is carried out through a systematic procedure. The resulting matrix equations are solved through an iteration process, carried out on a PC. Numerical results are presented for the hydrogen negative ion H-, the helium and helium-like ions(Z = 3 ~ 6) the hydrogen molecule ion H2+ and the positronium negative ion Ps-. Comparison with the variational and other approaches shows our results to be of comparable accuracy for the eigenenergies, but can yield highly accurate wave functions as by-products. Results on low-lying excited states are obtained simultaneously with the ground state properties with no extra effort. In particular, for the doubly excited states, such as1,3Pe, our method can give expectation values characterizing the three-body wave functions that have not been calculated before. As a general systematic approach to the three-body Coulomb problem, the solution process is reduced to a well-defined procedure that requires minimal human intervention (e.g., in the choice of basis functions for the variational approach), with well-demonstrated convergence.
Subjects/Keywords: Coulomb functions
; Quantum theory
; Mathematical physics
; Three-body problem
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APA (6^{th} Edition):
Chi, X. (2004). A non-variational approach to the quantum three-body coulomb problem. (Thesis). Hong Kong University of Science and Technology. Retrieved from http://repository.ust.hk/ir/Record/1783.1-2356 ; https://doi.org/10.14711/thesis-b849116 ; http://repository.ust.hk/ir/bitstream/1783.1-2356/1/th_redirect.html
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16^{th} Edition):
Chi, Xuguang. “A non-variational approach to the quantum three-body coulomb problem.” 2004. Thesis, Hong Kong University of Science and Technology. Accessed October 30, 2020.
http://repository.ust.hk/ir/Record/1783.1-2356 ; https://doi.org/10.14711/thesis-b849116 ; http://repository.ust.hk/ir/bitstream/1783.1-2356/1/th_redirect.html.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7^{th} Edition):
Chi, Xuguang. “A non-variational approach to the quantum three-body coulomb problem.” 2004. Web. 30 Oct 2020.
Vancouver:
Chi X. A non-variational approach to the quantum three-body coulomb problem. [Internet] [Thesis]. Hong Kong University of Science and Technology; 2004. [cited 2020 Oct 30].
Available from: http://repository.ust.hk/ir/Record/1783.1-2356 ; https://doi.org/10.14711/thesis-b849116 ; http://repository.ust.hk/ir/bitstream/1783.1-2356/1/th_redirect.html.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Chi X. A non-variational approach to the quantum three-body coulomb problem. [Thesis]. Hong Kong University of Science and Technology; 2004. Available from: http://repository.ust.hk/ir/Record/1783.1-2356 ; https://doi.org/10.14711/thesis-b849116 ; http://repository.ust.hk/ir/bitstream/1783.1-2356/1/th_redirect.html
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Delft University of Technology
26.
de Boer, Roderick (author).
Time-Optimal Transfers Between Planar Solar-Sail Libration Point Orbits.
Degree: 2020, Delft University of Technology
URL: http://resolver.tudelft.nl/uuid:c97e4c70-cf7a-4f7d-aed2-e2782b141e14
► This paper presents time-optimal transfer trajectories between planar solar-sail displaced libration point orbits around the L_{1} and L_{2} points of the Sun-Earth and Earth-Moon systems.…
(more)
▼ This paper presents time-optimal transfer trajectories between planar solar-sail displaced libration point orbits around the L_{1} and L_{2} points of the Sun-Earth and Earth-Moon systems. Initial guesses for these transfers are generated as two-segment trajectories, with a fixed sail attitude along each segment. The position and velocity discontinuity between the segments is minimized by means of a genetic-algorithm approach. The time of flight of these trajectories is then optimized by means of a direct pseudo-spectral collocation method as well as a multiple shooting differential correction (MSDC) method. The results of these methods are subsequently compared. Pseudo-spectral collocation was found to outperform MSDC in the solar-sail augmented Sun-Earth system, obtaining trajectories with transfer times as short as 101 days. Differential correction generally yields trajectories with slightly longer flight times than pseudo-spectral collocation, but converges more reliably. In the time-dependent solar-sail augmented Earth-Moon system, pseudo-spectral collocation fails to provide reproducible results. Transfer trajectories with flight times as short as 15.6 days are obtained in the Earth-Moon system using MSDC, but these trajectories feature control discontinuities that are likely to be problematic in practice.
Aerospace Engineering
Advisors/Committee Members: Heiligers, Jeannette (mentor), Delft University of Technology (degree granting institution).
Subjects/Keywords: Solar sailing; Circular restricted three-body problem; Libration point orbit; Optimal Control; Astrodynamics; Transfer orbits; Trajectory optimisation; Multiple shooting; Collocation
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APA (6^{th} Edition):
de Boer, R. (. (2020). Time-Optimal Transfers Between Planar Solar-Sail Libration Point Orbits. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:c97e4c70-cf7a-4f7d-aed2-e2782b141e14
Chicago Manual of Style (16^{th} Edition):
de Boer, Roderick (author). “Time-Optimal Transfers Between Planar Solar-Sail Libration Point Orbits.” 2020. Masters Thesis, Delft University of Technology. Accessed October 30, 2020.
http://resolver.tudelft.nl/uuid:c97e4c70-cf7a-4f7d-aed2-e2782b141e14.
MLA Handbook (7^{th} Edition):
de Boer, Roderick (author). “Time-Optimal Transfers Between Planar Solar-Sail Libration Point Orbits.” 2020. Web. 30 Oct 2020.
Vancouver:
de Boer R(. Time-Optimal Transfers Between Planar Solar-Sail Libration Point Orbits. [Internet] [Masters thesis]. Delft University of Technology; 2020. [cited 2020 Oct 30].
Available from: http://resolver.tudelft.nl/uuid:c97e4c70-cf7a-4f7d-aed2-e2782b141e14.
Council of Science Editors:
de Boer R(. Time-Optimal Transfers Between Planar Solar-Sail Libration Point Orbits. [Masters Thesis]. Delft University of Technology; 2020. Available from: http://resolver.tudelft.nl/uuid:c97e4c70-cf7a-4f7d-aed2-e2782b141e14
27.
Pousse, Alexandre.
Le quasi-satellites et autres configurations remarquables en résonance co-orbitale : Around quasi-satellites and remarkable configurations in the co-orbital resonance.
Degree: Docteur es, Mécanique céleste, 2016, Paris Sciences et Lettres (ComUE)
URL: http://www.theses.fr/2016PSLEO006
► L'ensemble des travaux menés au cours de cette thèse concerne l'étude de la résonance co-orbitale. Ce domaine de trajectoires particulières, où un astéroïde et une…
(more)
▼ L'ensemble des travaux menés au cours de cette thèse concerne l'étude de la résonance co-orbitale. Ce domaine de trajectoires particulières, où un astéroïde et une planète gravitent autour du Soleil avec la même période de révolution, possède une dynamique très riche liée aux célèbres configurations équilatérales de Lagrange, L4 et L5, ainsi qu'aux configurations alignées de Euler, L1, L2 et L3. Un exemple majeur dans le système solaire est donné par les astéroïdes « troyens » qui accompagnent Jupiter au voisinage des équilibres L4 et L5. Une deuxième configuration étonnante est donnée par les satellites Janus et Épiméthée qui gravitent autour de la planète Saturne ; suite à la forme décrite par la trajectoire d’un des satellites dans un repère tournant avec l’autre, la dynamique résultante est appelée « fer-à-cheval ». Un nouveau type de dynamique a été récemment misen évidence dans le contexte de la résonance coorbitale : les « quasi-satellites ». Il s’agit de configurations remarquables où, dans un repère tournant avec la planète, la trajectoire de l’astéroïde correspond à celle d’un satellite rétrograde. Des astéroïdes accompagnant les planètes Venus, Jupiter et la Terre ont notamment été observés dans ces configurations. La dynamique des quasi-satellites possède un grand intérêt, pas seulement parce qu’elle relie les différents domaines de la résonance co-orbitale (voir les travaux de Namouni, 1999) mais aussi parce qu’elle semble faire le pont entre les notions de satellisation et celles de trajectoires héliocentriques. Cependant, bien que le terme « quasi-satellite" soit devenu dominant dans la communauté de mécanique céleste, certains auteurs utilisent plutôt la terminologie « satellite rétrograde » révélant ainsi une ambiguïté sur la définition de ces trajectoires. Les récentes découvertes autour des exo-planètes ont motivé le développement de travaux concernant la résonance co-orbitale dans le problème des trois corps planétaire. Dans ce contexte Giuppone et al. (2010) ont mis en évidence (par une méthode numérique) les quasisatellites ainsi que des nouvelles familles de configurations remarquables : les orbites « anti-Lagrange ». La troisième partie de thèse présente alors une méthode analytique pour l'étude planétaire, permettant de révéler analytiquement les orbites anti-Lagrange ainsi qu'une esquisse d'étude des quasisatellites en adaptant à ce contexte plus général la méthode présentée dans la seconde partie. Pour ces raisons, la première partie de cette thèse a consisté à clarifier la définition de ces orbites en revisitant le cas circulaire-plan (trajectoires coplanaires avec la planète qui gravite sur une orbite circulaire) dans le cadre du problème moyen. Dans la deuxième partie de cette thèse, nous avons développé une méthode analytique apte à explorer le domaine des quasi-satellites dans le cadre du problème moyen. Nous avons réalisé cette exploration dans le cas circulaire-plan et proposé une extension aux cas excentrique-plan et circulaire-spatial.
This work of thesis focuses on the study of…
Advisors/Committee Members: Robutel, Philippe (thesis director), Vienne, Alain (thesis director).
Subjects/Keywords: Mécanique céleste; Résonance co-Orbitale; Problème à trois corps; Celestial mechanics; Co-Orbital resonance; Three-Body problem; 520
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APA (6^{th} Edition):
Pousse, A. (2016). Le quasi-satellites et autres configurations remarquables en résonance co-orbitale : Around quasi-satellites and remarkable configurations in the co-orbital resonance. (Doctoral Dissertation). Paris Sciences et Lettres (ComUE). Retrieved from http://www.theses.fr/2016PSLEO006
Chicago Manual of Style (16^{th} Edition):
Pousse, Alexandre. “Le quasi-satellites et autres configurations remarquables en résonance co-orbitale : Around quasi-satellites and remarkable configurations in the co-orbital resonance.” 2016. Doctoral Dissertation, Paris Sciences et Lettres (ComUE). Accessed October 30, 2020.
http://www.theses.fr/2016PSLEO006.
MLA Handbook (7^{th} Edition):
Pousse, Alexandre. “Le quasi-satellites et autres configurations remarquables en résonance co-orbitale : Around quasi-satellites and remarkable configurations in the co-orbital resonance.” 2016. Web. 30 Oct 2020.
Vancouver:
Pousse A. Le quasi-satellites et autres configurations remarquables en résonance co-orbitale : Around quasi-satellites and remarkable configurations in the co-orbital resonance. [Internet] [Doctoral dissertation]. Paris Sciences et Lettres (ComUE); 2016. [cited 2020 Oct 30].
Available from: http://www.theses.fr/2016PSLEO006.
Council of Science Editors:
Pousse A. Le quasi-satellites et autres configurations remarquables en résonance co-orbitale : Around quasi-satellites and remarkable configurations in the co-orbital resonance. [Doctoral Dissertation]. Paris Sciences et Lettres (ComUE); 2016. Available from: http://www.theses.fr/2016PSLEO006
Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ)
28.
Antoniadou, Kyriaki.
Dynamics of planetary systems in resonances: from the planar to the spatial case.
Degree: 2014, Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ)
URL: http://hdl.handle.net/10442/hedi/34917
► Over the last decades, there has been a tremendous increase of extrasolar planetary systems discoveries. Many of such systems consist of more than one planet…
(more)
▼ Over the last decades, there has been a tremendous increase of extrasolar planetary systems discoveries. Many of such systems consist of more than one planet and the study of planetary orbits concerning their long-term stability is very interesting. Also, many planets seem to be locked in mean motion resonance (MMR). The aim of this thesis is to utilize the model of spatial general three body problem (GTBP), in order to simulate such resonant systems through the computation of periodic orbits. We figure out regions where the planets in resonances should be ideally hosted in favour of long-term stability and therefore, survival. In other words, we analyze planar and spatial symmetric and asymmetric configurations of systems consisting of a star and two planets or a planet and an asteroid by computing families of periodic orbits in each case. These families are obtained through analytic continuation schemes and the linear horizontal and vertical stability of periodic orbits is studied. Particularly, in the elliptic restricted TBP (ERTBP) and for the cases of 1/2, 1/3 and 3/2 resonances, we showed how asymmetric families are generated through two types of bifurcation points, belonging either to symmetric families of the ERTBP or to asymmetric ones of the circular restricted TBP (CRTBP). In the planar GTBP, we depicted the way the evaluation of a continuation scheme alters the topological structure of the families: either modifying their overall shape, or forming gaps, which interrupt their smooth emanation from the bifurcation point. Moreover, we performed a thorough application of continuation schemes by varying, on the one hand, the mass of the initially massless body (starting from spatial CRTBP) and on the other, the third dimension or (equivalently) the inclination (starting from the planar TBP). In the first case, we observed the formation of closed loops and foldings, which result in the generation of three dimensional families evolving exclusively in space, i.e. they cannot be generated by continuation schemes described above. Additionally, we calculated both planar and spatial families of symmetric periodic orbits, along with their stability, for meaningful planets' mass ratios for all the MMR values into which the extrasolar planets are found to be locked (4/3, 3/2, 2/1, 5/2, 3/1 and 4/1) and 1/1, as well, and every possible configuration. Furthermore, we provided evidence that resonant inclined planets should be connected with a migration Type II mechanism, which involves the passage of the planets from the vertical critical periodic orbits (v.c.o.) - after resonant capture - with the inclination resonance, which takes effect when the planets' inclinations increase and the respective resonant angles librate. Given the mass ratio and the eccentricities of the planets, then, we can conclude whether the system had passed through a v.c.o. and thus, would have a non-zero mutual inclination. Finally, we relate the long-term dynamical stability of fictitious planetary systems with the evolution in the vicinity of…
Subjects/Keywords: Εξωπλανητικά συστήματα; Πρόβλημα τριών σωμάτων; Συντονισμένη κίνηση; Πλανητική μετανάστευση; Exoplanetary systems; Three body problem; Resonant motion; Planetary migration
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APA (6^{th} Edition):
Antoniadou, K. (2014). Dynamics of planetary systems in resonances: from the planar to the spatial case. (Thesis). Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ). Retrieved from http://hdl.handle.net/10442/hedi/34917
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16^{th} Edition):
Antoniadou, Kyriaki. “Dynamics of planetary systems in resonances: from the planar to the spatial case.” 2014. Thesis, Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ). Accessed October 30, 2020.
http://hdl.handle.net/10442/hedi/34917.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7^{th} Edition):
Antoniadou, Kyriaki. “Dynamics of planetary systems in resonances: from the planar to the spatial case.” 2014. Web. 30 Oct 2020.
Vancouver:
Antoniadou K. Dynamics of planetary systems in resonances: from the planar to the spatial case. [Internet] [Thesis]. Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ); 2014. [cited 2020 Oct 30].
Available from: http://hdl.handle.net/10442/hedi/34917.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Antoniadou K. Dynamics of planetary systems in resonances: from the planar to the spatial case. [Thesis]. Aristotle University Of Thessaloniki (AUTH); Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ); 2014. Available from: http://hdl.handle.net/10442/hedi/34917
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Texas – Austin
29.
-9883-5836.
Patched periodic orbits : a systematic strategy for low-energy trajectory and moon tour design.
Degree: PhD, Aerospace Engineering, 2018, University of Texas – Austin
URL: http://hdl.handle.net/2152/68679
► The implementation of low-energy trajectories has opened a new paradigm in trajectory design, where, at the cost of long transfer times, low-fuel consumption missions opened…
(more)
▼ The implementation of low-energy trajectories has opened a new paradigm
in trajectory design, where, at the cost of long transfer times, low-fuel consumption
missions opened a new world of routes for space exploration. Low-cost
lunar missions and the exploration of the gas giant planetary satellite
systems are one of the main applications of these fuel-efficient trajectories.
However, the flexibility in applications that low-energy trajectories provide
comes at the cost of high complexity in the design. In this dissertation a
systematic strategy to simplify the design process of low-energy trajectories
is developed. The method, called patched periodic orbits (PPO) is analogous to the patched-conics model in high energy regimes, where conic segments are used as building blocks to give rise to full complex trajectories. In the PPO model, the building blocks are precomputed
three-
body periodic orbits that are patched together to build transfer mechanisms in multi-
body environments.
To support the PPO model, a broad database of axisymmetric
three-
body
periodic orbits for planets and main planetary satellites in the Solar
System have been generated and provided online. The periodic orbit search
is performed over 24 pairs of bodies that are well approximated by the circular
restricted
three-
body problem, resulting in approximately 3 million periodic
solutions. The database contains a new set of periodic solutions that
approximate heteroclinic connections between other pairs of periodic orbits.
These connecting orbits provide free escape/capture mechanisms as well as
natural transfers between libration point orbits, among others. In order to
efficiently converge the highly sensitive solutions the database is generated using
a multiple grid search strategy and a robust differential corrector with a
full second-order trust region method.
Examples of point design applications for several different challenging
trajectory problems are introduced, including transfers between the Galilean
moons, alternative endgames of a Europa mission, and low-cost Earth-Moon transfers with ballistic lunar captures. Additionally, a strategy to compute landing trajectories at Europa with a broad surface coverage is presented. The strategy uses lissajous segments as staging orbits that allow to decouple the landing phase with the Europa approach. Combining the PPO model and the landing strategy, an end-to-end solution that connects the landing phase, the staging orbit, and a Ganymede-Europa moon tour is presented.
Advisors/Committee Members: Russell, Ryan P., 1976- (advisor), Fowler, Wallece T. (committee member), Akella, Maruthi R. (committee member), Bettadpur, Srinivas V. (committee member), Lo, Martin (committee member).
Subjects/Keywords: Low-energy trajectory; Astrodynamics; Celestial mechanics; Circular restricted three-body problem; Periodic orbits; Mission design; Trajectory optimization; Galilean moon tours
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APA (6^{th} Edition):
-9883-5836. (2018). Patched periodic orbits : a systematic strategy for low-energy trajectory and moon tour design. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/68679
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Chicago Manual of Style (16^{th} Edition):
-9883-5836. “Patched periodic orbits : a systematic strategy for low-energy trajectory and moon tour design.” 2018. Doctoral Dissertation, University of Texas – Austin. Accessed October 30, 2020.
http://hdl.handle.net/2152/68679.
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
MLA Handbook (7^{th} Edition):
-9883-5836. “Patched periodic orbits : a systematic strategy for low-energy trajectory and moon tour design.” 2018. Web. 30 Oct 2020.
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Vancouver:
-9883-5836. Patched periodic orbits : a systematic strategy for low-energy trajectory and moon tour design. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2018. [cited 2020 Oct 30].
Available from: http://hdl.handle.net/2152/68679.
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Council of Science Editors:
-9883-5836. Patched periodic orbits : a systematic strategy for low-energy trajectory and moon tour design. [Doctoral Dissertation]. University of Texas – Austin; 2018. Available from: http://hdl.handle.net/2152/68679
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Queens University
30.
Mansur, Abdalla.
Instability of Periodic Orbits of Some Rhombus and Parallelogram Four Body Problems
.
Degree: Mathematics and Statistics, 2012, Queens University
URL: http://hdl.handle.net/1974/7650
► The rhombus and parallelogram orbits are interesting families of periodic solutions, which come from celestial mechanics and the N-body problem. Variational methods with finite order…
(more)
▼ The rhombus and parallelogram orbits are interesting families of periodic solutions, which come from celestial mechanics and the N-body problem. Variational methods with finite order symmetry group are used to construct minimizing non-collision periodic orbits.
We study the question of stability or instability of periodic and symmetric periodic solutions of the rhombus and the equal mass parallelogram four body problems. We first study the stability of periodic solutions for the rhombus four body problem. An analytical description of the variational principle is used to show that the homographic solutions are the minimizers of the action functional restricted to rhombus loop space [23]. We employ techniques from symplectic geometry and specifically a variant of the Maslov index for curves of Lagrangian subspaces along the minimizing rhombus orbit to prove the main result, Theorem 4.2.2, which states that the reduced rhombus orbit is hyperbolic in the reduced energy manifold when it is not degenerate.
We second study the stability for symmetric periodic solutions of the equal mass parallelogram four body problem. The parallelogram family is a family of Z_2× Z_4 symmetric action minimizing solutions, investigated by [7]. In this example, the minimizing solution [7] can be extended to a 4T-periodic solution using symmetries through square and collinear configurations. The Maslov index of the orbits is used to prove the main result, Theorem 5.3.1, which states that the minimizing equal mass parallelogram solution is unstable when it is non-degenerate.
Subjects/Keywords: N-Body Problem
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APA (6^{th} Edition):
Mansur, A. (2012). Instability of Periodic Orbits of Some Rhombus and Parallelogram Four Body Problems
. (Thesis). Queens University. Retrieved from http://hdl.handle.net/1974/7650
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16^{th} Edition):
Mansur, Abdalla. “Instability of Periodic Orbits of Some Rhombus and Parallelogram Four Body Problems
.” 2012. Thesis, Queens University. Accessed October 30, 2020.
http://hdl.handle.net/1974/7650.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7^{th} Edition):
Mansur, Abdalla. “Instability of Periodic Orbits of Some Rhombus and Parallelogram Four Body Problems
.” 2012. Web. 30 Oct 2020.
Vancouver:
Mansur A. Instability of Periodic Orbits of Some Rhombus and Parallelogram Four Body Problems
. [Internet] [Thesis]. Queens University; 2012. [cited 2020 Oct 30].
Available from: http://hdl.handle.net/1974/7650.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Mansur A. Instability of Periodic Orbits of Some Rhombus and Parallelogram Four Body Problems
. [Thesis]. Queens University; 2012. Available from: http://hdl.handle.net/1974/7650
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
◁ [1] [2] [3] [4] [5] … [847] ▶
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