Modern Astrodynamics

3

Solving Two-Point Boundary Value Problems Using Generating Functions: Theory and Applications to Astrodynamics

VINCENT M. GUIBOUT ^*

^*MBDA France

DANIEL J. SCHEERES ^†

^†University of Michigan, Ann Arbor, Michigan.

Contents

3.1. Introduction

3.2. Solving two-point boundary value problems

3.3. Hamilton’s principal function

3.4. Local solutions of the Hamilton–Jacobi equation

3.5. Applications

3.6. Conclusions

Appendix A. The Hamilton–Jacobi equation at higher orders

Appendix B. The Hill three-body problem

References

3.1 Introduction

Two-point boundary value problems have a central place in the field of astrodynamics. In general, most of the hard problems in this field revolve around solving such problems. Examples include the targeting ...