3. The Kustaanheimo–Stiefel space and the Hopf fibration

Kapitel in diesem Buch

1. Frontmatter I
2. Foreword VII
3. Contents IX
4. 1. Introduction. Current challenges in space exploration 1
5. Part I: Regularization
6. 2. Theoretical aspects of regularization 11
7. 3. The Kustaanheimo–Stiefel space and the Hopf fibration 47
8. 4. The Dromo formulation 84
9. 5. Dedicated formulation: Propagating hyperbolic orbits 101
10. 6. Evaluating the numerical performance 127
11. Part II: Applications
12. 7. The theory of asynchronous relative motion 141
13. 8. Universal and regular solutions to relative motion 172
14. 9. Generalized logarithmic spirals: A new analytic solution with continuous thrust 195
15. 10. Lambert’s problem with generalized logarithmic spirals 233
16. 11. Low-thrust trajectory design with controlled generalized logarithmic spirals 261
17. 12. Nonconservative extension of Keplerian integrals and new families of orbits 293
18. 13. Conclusions 324
19. Part III: Appendices
20. A. Hypercomplex numbers 327
21. B. Formulations in PERFORM 336
22. C. Stumpff functions 339
23. E. Elliptic integrals and elliptic functions 348
24. F. Controlled generalized logarithmic spirals 356
25. G. Dynamics in Seiffert’s spherical spirals 366
26. List of Figures 379
27. Bibliography 383
28. Index 399