Polyhedral potential and variational integrator computation of the full two body problem

Collection of Technical Papers - AIAA/AAS Astrodynamics Specialist Conference, 2006

Volumn 1, Issue , 2006, Pages 644-660

  Fahnestock, Eugene G ^a,b   Lee, Taeyoung ^a,b   Leok, Melvin ^a   McClamroch, N Harris ^a,b   Scheeres, Daniel J ^a,b  

^a UNIVERSITY OF MICHIGAN   (United States)

^b AIAA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; COMPUTER SIMULATION; EQUATIONS OF MOTION; GRAVITATION; INTEGRATION;

GEOMETRIC FEATURES; LIE GROUP VARIATIONAL INTEGRATOR (LGVI); TWO BODY PROBLEM; VARIATIONAL INTEGRATOR COMPUTATION;

ASTRONOMY;

EID: 33845973682     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.2514/6.2006-6289     Document Type: Conference Paper

References (31)

1. Werner, R. A. and Scheeres, D. J., "Mutual Potential of Homogenous Polyhedra," Celestial Mechanics and Dynamical Astronomy, Vol. 91, No. 3, March 2005, pp. 337-349.
2. Bottke, W. F. and Melosh, H. J., "The Formation of Binary Asteroids and Doublet Craters," Icarus, Vol. 124, 1996, pp. 372391.
3. Bottke, W. F. and Melosh, H. J., "The Formation of Asteroid Satellites and Doublet Craters by Planetary Tidal Forces," Nature, Vol. 381, 1996, pp. 5153.
4. Margot, J. L., Nolan, M. C., Benner, L. A. M., Ostro, S. J., Jurgens, R. F., Giorgini, J. D., Slade, M. A., and Campbell, D. B., "Binary Asteroids in the Near-Earth Object Population," Science, Vol. 296, May 2002, pp. 1445-1448.
5. Merline, W. J., Weidenschilling, S. J., Durda, D. D., Margot, J. L., Pravec, P., and Storrs, A. D., "Asteroids do have satellites," Asteroids III, edited by W. F. Bottke et al., Space Science Series, University of Arizona, Tuscon, AZ, 2002, pp. 289-312.
6. Ostro, S. J., Hudson, R. S., Benner, L. A. M., Giorgini, J. D., Magri, C., Margot, J.-L., and Nolan, M. C., "Asteroid Radar Astronomy," Asteroids III, edited by W. F. Bottke et al., Space Science Series, University of Arizona, Tuscon, AZ, 2002, pp. 151-168.
7. Maciejewski, A. J., "Reduction, Relative Equilibria and Potential in the Two Rigid Bodies Problem," Celestial Mechanics and Dynamical Astronomy, Vol. 63, No. 1, 1995, pp. 1-28.
8. Scheeres, D. J., "Stability in the Full Two-Body Problem," Celestial Mechanics and Dynamical Astronomy, Vol. 83, 2002, pp. 155-169.
9. Scheeres, D. J., "Stability of Relative equilibria in the Full Two-Body Problem," New Trends in Astrodynamics Conference, Jan. 2003.
10. Scheeres, D. J. and Augenstein, S., "Spacecraft motion about binary asteroids," Proc. AAS/AIAA Astrodynamics Specialist Conference, Aug. 2003.
11. Gabern, F., Koon, W. S., and Marsden, J. E., "Spacecraft dynamics near a binary asteroid," Proceedings of the fifth international conference on dynamical systems and differential equations, Jun 2004.
12. Scheeres, D. J. and Bellerose, J., 'The Restricted Hill Full 4-Body Problem: application to spacecraft motion about binary asteroids," Dynamical Systems: An International Journal, Vol. 20, No. 1, 2005, pp. 23-44.
13. Borderies, N., "Mutual gravitational potential of N solid bodies," Celestial Mechanics, Vol. 18, No. 3, 1978, pp. 295-307.
14. Braun, C. V., The gravitational potential of two arbitrary, rotating bodies with applications to the Earth-Moon system, Ph.D. thesis, University of Texas at Austin, 1991.
15. Moritz, H., Advanced Physical Geodesy, Abacus Press, 1980.
16. Geissler, P., Petit, J.-M., Durda, D. D., Greenberg, R., Bottke, W., Nolan, M., and Moore, J., "Erosion and Ejecta Reaccretion of 243 Ida and Its Moon," Icarus, Vol. 120, No. 1, 1996, pp. 140-157.
17. Ashenberg, J., "Proposed Method for Modeling the Gravitational Interaction Between Finite Bodies," Journal of Guidance, Control, and Dynamics, Vol. 28, No. 4, 2005, pp. 768-774.
18. Werner, R. A. and Scheeres, D. J., "Exterior Gravitation of a Polyhedron Derived and Compared with Harmonic and Mascon Gravitation Representations of Asteroid 4769 Castalia," Celestial Mechanics and Dynamical Astronomy, Vol. 65, No. 3, 1997, pp. 313-344.
19. Fahnestock, E. G., Scheeres, D. J., McClamroch, N. H., and Werner, R. A., "Simulation and Analysis of Binary Asteroid Dynamics Using Mutual Potential and Potential Derivatives Formulation," Proc. AAS/AIAA Astrodynamics Specialist Conference, Lake Tahoe, CA, Aug. 2005.
20. Fahnestock, E. G. and Scheeres, D. J., "Simulation of the Full Two Rigid Body Problem Using Polyhedral Mutual Potential and Potential Derivatives Approach," Celestial Mechanics and Dynamical Astronomy, submitted for publication.
21. Hairer, E., Lubich, C., and Wanner, G., Geometric Numerical Integration, Springer, 2000.
22. Marsden, J. E. and West, M., "Discrete mechanics and variational integrators," Acta Numerica, Vol. 10, 2001, pp. 357-514.
23. Iserles, A., Munthe-Kaas, H. Z., Nørsett, S. P., and Zanna, A., "Lie-group methods," Acta Numerica, Vol. 9, 2000, pp. 215-365.
24. Lee, T., Leok, M., and McClamroch, N. H., "A Lie group variational integrator for the attitude dynamics of a rigid body with application to the 3D pendulum," Proceedings of the IEEE Conference on Control Application, Toronto, Canada, Aug. 2005, pp. 962-967.
25. Lee, T., Leok, M., and McClamroch, N. H., "Lie group variational integrators for the Full Body Problem," Computer Methods in Applied Mechanics and Engineering, submitted, Available: http://arxiv.org/abs/math. NA/0508365.
26. Yeomans, D. K. et al., "Radio Science Results During the NEAR-Shoemaker Spacecraft Rendezvous with Eros," Science, Vol. 289, Sept. 2000, pp. 2085-2088.
27. Fujiwara, A., Kawaguchi, J., Yeomans, D. K., Abe, M., Mukai, T., Okada, T., Saito, J., Yano, H., Yoshikawa, M., Scheeres, D. J., Barnouin-Jha, O., Cheng, A. F., Demura, H., Gaskell, R. W., Hirata, N., Ikeda, H., Kominato, T., Miyamoto, H., Nakamura, A. M., Nakamura, R., Sasaki, S., and Uesugi, K., "The Rubble-Pile Asteroid Itokawa as Observed by Hayabusa," Science, accepted for publication.
28. Richardson, D. C., William F. Bottke, J., and Love, S. G., "Tidal Distortion and Disruption of Earth-Crossing Asteroids," Icarus, Vol. 134, 1998, pp. 47-76.
29. Roig, F., Duffard, R., Penteado, P., Lazzaro, D., and Kodama, T., "Interacting ellipsoids: a minimal model for the dynamics of rubble-pile bodies," Icarus, Vol. 165, No. 2, 2003, pp. 355-370.
30. Korycansky, D. G., "Orbital Dynamics for Rigid Bodies," Astrophysics and Space Science, Vol. 291, 2004, pp. 57-74
31. Duan, Z.-H. and Krasny, R., "An Adaptive Treecode for Computing Nonbonded Potential Energy in Classical Molecular Systems," Journal of Computational Chemistry, Vol. 22, No, 2, 2001, pp. 184-195