Canonical modelling of relative spacecraft motion via epicyclic orbital elements

Celestial Mechanics and Dynamical Astronomy

Volumn 92, Issue 4, 2005, Pages 337-370

  Kasdin, N Jeremy ^a   Gurfil, Pini ^b   Kolemen, Egemen ^a  

^a Princeton University   (United States)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Formation flying; Hamiltonian dynamics; Perturbations; Relative motion

Indexed keywords

EID: 26944440670     PISSN: 09232958     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10569-004-6441-7     Document Type: Article

References (20)

1. Alfriend, K. and Schaub, H.: 2000, 'Dynamics and control of spacecraft formations: challenges and some solutions', J. Astronaut. Sci. 48(2), 249-267.
2. Alfriend, K. and Yan, H.: 2002, 'An orbital elements approach to the nonlinear formation flying problem', In: International Formation Flying Symposium, Toulouse, France.
3. Battin, R.: 1999, An Introduction to the Mathematics and Methods of Astrodynamics, AIAA.
4. Born, G. H.: 2001, 'Motion of a Satellite under the influence of an Oblate Earth'. Technical Report ASEN 3200, University of Colorado, Boulder.
5. Carter, T. and Humi, M.: 1987, 'Fuel-optimal rendezvous near a point in general Keplerian orbit', J. Guidance, Control Dynam. 10(6), 567-573.
6. Clohessy, W. and Wiltshire, R.: I960, 'Terminal guidance system for satellite rendezvous.' J. Astronaut. Sci. 27(9), 653-678.
7. Efroimsky, M. and Goldreich, P.: 2003, 'Gauge symmetry of the N-body problem in the Hamilton-Jacobi approach', J. Math. Phys. 44, 5958-5977.
8. Efroimsky, M. and Goldreich, P.: 2004, 'Gauge freedom in the N-body problem of celestial mechanics', Astron. Astrophys. 415, 1187-1899.
9. Gim, D. and Alfriend, K.: 2001, 'The state transition matrix of relative motion for the perturbed non-circular reference Orbit', In: Proceedings of the AAS/AIAA Space Flight Mechanics Meeting, Santa Barbara, CA.
10. Goldstein, H.: 1980, Classical Mechanics. Addison-Wesley.
11. Gurfil, P. and Kasdin, N.: 2004, 'Nonlinear modeling and control of spacecraft relative motion in the configuration space', J. Guidance, Control, Dynam. 27(1), 154-157.
12. Hill, G.: 1878, 'Researches in the lunar theory'. Am. J Math. 1, 5-26.
13. Inalhan, G., Tillerson, M. and How, J.: 2002, 'Relative dynamics and control of spacecraft formations in eccentric orbits', J. Guidance, Control Dynam. 25(1), 48-60.
14. Karlgaard, C. and Lutze, F.: 2001, 'Second-order relative motion equations'. In: Proceedings of the AAS/AIAA Astrodynamics Conference, Quebec City, Quebec.
15. Kasdin, N. and Gurfil, P.: 2004, 'Hamiltonian modeling of relative motion'. In: E. Belbruno, D. Folta and P. Gurfil (eds.), Astrodynamics, Space Missions, and Chaos, The Annals of the New York Academy of Sciences, Vol. 1017.
16. Namouni, F.: 1999, 'Secular interactions of coorbiting objects', Icarus 137, 293-314.
17. 2 invariant relative orbits for spacecraft formations', Celes. Mech. Dynam. Astron. 79, 77-95.
18. Schaub, H., Vadali, S. and Alfriend K.: 2000, 'Formation flying control using mean orbital elements', J. Astronaut. Sci. 48(1), 69-87.
19. Scheeres, D., Hsiao, F. and Vinh, N.: 2003, 'Stabilizing motion relative to an unstable orbit: Applications to spacecraft formation flight', J. Guidance, Control Dynam. 26(1), 62-73.
20. Vinti, J. P.: 1998, Orbital and Celestial Mechanics, Progress in Astronautics and Aeronautics, Vol. 177, AIAA.