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Tables of Contents for Dynamics and Mission Design Near Libration Points
Chapter/Section Title
Page #
Page Count
Preface
v
 
Bibliographical Survey
1
14
Equations. The Triangular Equilibrium Points and their Stability
1
1
Numerical Results for the Motion Around L4 and L5
2
4
Analytical Results for the Motion Around L4 and L5
6
6
The Models Used
6
6
Miscellaneous Results
12
3
Station Keeping at the Triangular Equilibrium Points
12
1
Some Other Results
12
3
Periodic Orbits of the Bicircular Problem and Their Stability
15
18
Introduction
15
1
The Equations of the Bicircular Problem
16
3
Periodic Orbits with the Period of the Sun
19
2
The Tools: Numerical Continuation of Periodic Orbits and Analysis of Bifurcations
21
7
Numerical Continuation of Periodic Orbits for Nonautonomous and Autonomous Equations
21
3
Bifurcations of Periodic Orbits: From the Autonomous to the Nonautonomous Periodic System
24
2
Bifurcation for Eigenvalues Equal to One
26
2
The Periodic Orbits Obtained by Triplication
28
5
Numerical Simulations of the Motion in an Extended Neighborhood of the Triangular Libration Points in the Earth-Moon System
33
14
Introduction
34
1
Simulations of Motion Starting at the Instantaneous Triangular Points at a Given Epoch
35
1
Simulations of Motion Starting Near the Planar Periodic Orbit of Kolenkiewicz and Carpenter
35
12
The Equations of Motion
47
24
Reference Systems
47
1
The Lagrangian
48
3
The Hamiltonian and the Related Expansions
51
1
Some Useful Expansions
52
2
Fourier Analysis: The Relevant Frequencies and the Related Coefficients
54
8
Concrete Expansions of the Hamiltonian and the Functions
62
3
Simplified Normalized Equations. Tests
65
6
Tests of the Simplified Normalized Equations
66
5
Periodic Orbits of Some Intermediate Equations
71
16
Equations of Motion for the Computation of Intermediate Periodic Orbits
71
2
Obtaining the Periodic Orbits Around the Triangular Libration Points for the Intermediate Equations
73
1
Results and Comments
74
13
Quasi-periodic Solution of the Global Equations: Semianalytic Approach
87
20
The Objective
87
1
The Algorithm
88
2
The Adequate Set of Relevant Frequencies
90
4
Avoiding Secular Terms
94
1
The Coefficients Related to the Different Frequencies
94
1
Determination of the Coefficients of Quasi-periodic Functions Using FFT
95
8
Results and Conclusions
103
4
Numerical Determination of Suitable Orbits of the Simplified System
107
14
The Objective
107
1
Description of Two Families of Algorithms. Reduction of the Linearized Equations
108
4
Description of the Methods. Comments
112
4
Results and Discussion
116
5
Relative Motion of Two Nearby Spacecrafts
121
16
The Selection of Orbits for the Two Spacecrafts
121
1
Variations of the Relative Distance and Orientation. Results
122
13
Comments on the Applicability of the Results
135
2
Summary
137
6
Objectives of the Work
137
1
Contribution to the Solution of the Problem
138
2
Conclusions
140
1
Outlook
141
2
Bibliography
143