Recent Advances in Celestial and Space Mechanics 1st Edition by Bernard Bonnard,Monique Chyba 3319274627 9783319274621

1 Introduction

2 The Colinear 3 Body Problem

2.1 Central Configurations

2.2 Non-integrability

2.3 Higher Variational Equations

3 The 4 Body Problem

3.1 Eigenvalue Bounding

3.2 Symmetric Central Configurations

3.3 Reduction of Exceptional Curves

3.4 Second Order Variational Equations

4 Higher Variational Equations

4.1 An Invariant Subspace of the 5-th Order Variational Equation

4.2 The Case {9,20}

5 The Planar n-Body Problem

6 Integrable n-Body Problems

6.1 An Integrable 5 Body Problem

6.2 An Integrable n+3 Body Problem

References

Relative Equilibria in the Full N-Body Problem with Applications to the Equal Mass Problem

1 Introduction

2 Fundamental Quantities and Specification of the Full N-Body Problem

2.1 Implicit Energy Dissipation Interaction Models

2.2 Density Distributions and Fundamental Quantities

2.3 Relative Reduction

2.4 Degrees of Freedom

2.5 Transformation into a Rotating System

2.6 Additional Integrals of Motion

3 Equilibrium and Stability Conditions

3.1 No Contact Case

3.2 Contact Case

4 Fundamental Quantities in the Full N-Body Problem

4.1 Rigid Body Expressions

4.2 Finite Density Sphere Restriction

4.3 Normalization

5 N=2

5.1 Equilibria and Stability

5.2 Hill Stability Conditions

6 N=3

6.1 Equilibria and Stability

6.2 Hill Stability Conditions

7 N=4

7.1 Equilibria and Stability

7.2 Static Rest Configurations

7.3 Mixed Equilibrium Configurations

7.4 Transitions Between Resting and Mixed Configurations

7.5 Compilation of Possible Relative Equilibria

7.6 Hill Stability Conditions

8 Summary

References

Station Keeping Strategies for a Solar Sail in the Solar System

1 Introduction

2 Dynamical Models

2.1 Restricted Three Body Problem for a Solar Sail

2.2 N-Body Problem for a Solar Sail

2.3 The Solar Sail

3 Background on the RTBPS

3.1 Equilibrium Points

3.2 Periodic Orbits

4 Station Keeping Strategy

4.1 Station Keeping in the RTBPS

4.2 Station Keeping in the NBPS

5 Mission Application

5.1 Mission Results

6 Conclusions

References

Minimum Fuel Round Trip from a L2 Earth-Moon Halo Orbit to Asteroid 2006 RH120

1 Introduction

2 Equations of Motion

3 Problem Statement

3.1 Approach Transfer

3.2 Return Transfer

3.3 Necessary Conditions for Optimality

3.4 Numerical Method

4 Numerical Results

4.1 Approach Transfer

4.2 Return Transfer from 2006 RH120 to L2

4.3 Complete Round Trip Mission

References

Low-Thrust Transfers Between Libration Point Orbits Without Explicit Use of Manifolds

1 Introduction

2 Problem Statement

2.1 Equations of Motion

2.2 Optimal Control Problem

2.3 Necessary Optimality Conditions

3 New Approach for Computing Low-Energy Transfers

3.1 Introduction

3.2 Three-Step Solution Method

4 Numerical Results

4.1 Orbits with Same Energy

4.2 Orbits with Different Energies

5 Conclusion

References

Time-Minimum Control of the Restricted Elliptic Three-Body Problem Applied to Space Transfer

1 Introduction

2 The Controlled Planar Elliptic Restricted Three-Body Problem

2.1 Controlled Equations of the Planar Circular Restricted Three-Body Problem

2.2 Controlled Equations of the Planar Elliptic Restricted Three-Body Problem

3 Controllability

4 Structure of the Optimal Control

4.1 Optimality Conditions

4.2 Singular Flow and Structure of Extremals

5 Application to Space Transfers

5.1 Numerical Methods

5.2 Numerical Computations

6 Conclusion

References

On Local Optima in Minimum Time Control of the Restricted Three-Body Problem

1 Introduction

2 Transfer from a GEO to L1

2.1 Fixed Initial Point on a GEO

2.2 Free Initial Point on a GEO

2.3 Cut Points

3 Transfer from a GEO to MO

3.1 Fixed Initial Point on a GEO

3.2 Free Initial Point on a GEO

3.3 Cut Points

3.4 Homotopy w.r.t r1

4 Conclusion

5 Tables for GEO to L1 Transfer Problem

6 Tables from GEO to MO Transfer Problem

7 Summary of the Cut Points on the GEO to L1 Transfer

8 Summary of the Cut Points on the GEO to MO Transfer

8.1 mathcalC1 Cut Points

8.2 mathcalC2 Cut Points