Geometric mechanics and the dynamics of asteroid pairs

Dynamical Systems

Volumn 20, Issue 1, 2005, Pages 3-21

  Cendra, H ^a   Marsden, J E ^b  

^a UNIVERSIDAD NACIONAL DEL SUR   (Argentina)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; GRAVITATION; HAMILTONIANS; LAGRANGE MULTIPLIERS; MATHEMATICAL MODELS; MATRIX ALGEBRA; POISSON DISTRIBUTION; PROBLEM SOLVING; SPACE FLIGHT;

ASTEROIDS; EUCLIDEAN GROUP; GEOMETRIC MECHANICS; POISSON BRACKETS;

ASTRONOMY;

EID: 12344335929     PISSN: 14689367     EISSN: None     Source Type: Journal    
DOI: 10.1080/1468936042000269578     Document Type: Article

References (25)

1. 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., 2002, Binary asteroids in the near-earth object population. Science, 296, 1445-1448.
2. Merline, W.J., Weidenschilling, S.J., Durda, D.D., Margot, J.L., Pravec, P. and Storrs, A.D., 2002, Asteroids do have satellites. In: W.M. Bottke, A. Cellino, P. Paolicchi and R.P. Binzel (Eds.) Asteroids III, pp. 289-312 (Tucson: University of Arizona Press).
3. Veillet, C., Parker, J.W., Griffin, I., Marsden, B., Doressoundiram, A., Buie, M., Tholen, D.J., Connelley, M. and Holman, M.J., 2002, The binary Kuiper-belt object 1998 ww31. Nature, 416, 711-713.
4. Koon, W.-S., Marsden, J.E., Ross, S., Lo, M. and Scheeres, D.J., 2004, Geometric mechanics and the dynamics of asteroid pairs. New York Academy of Sciences, 1017, 11-38.
5. Scheeres, D.J., Ostro, S.J., Werner, R.A., Asphaug, E. and Hudson, R.S., 2000, Effects of gravitational interactions on asteroid spin states, Icarus, 147, 106-118.
6. Scheeres, D.J., 2001, Changes in rotational angular momentum due to gravitational interactions between two finite bodies. Celestial Mechanics and Dynamical Astronomy, 81, 39-44.
7. Scheeres, D.J., 2002a, Stability in the full two-body problem. Celestial Mechanics and Dynamical Astronomy, 83, 155-169.
8. Scheeres, D.J., 2002b, Stability of binary asteroids. Icarus, 159, 271-283.
9. Scheeres, D.J., 2004, Stability of relative equilibria in the full two-body problem. Annals of the New York Academy of Science, 1017.
10. Cendra, H., Marsden, J.E. and Ratiu, T.S., 2001, Lagrangian Reduction by Stages, Vol. 152 of Memoirs (Providence, RI: American Mathematical Society).
11. Simo, J.C., Lewis, D.R. and Marsden, J.E., 1991, Stability of relative equilibria I: The reduced energy momentum method. Archive for Rational Mechanics and Analysis, 115, 15-59.
12. Marsden, J.E., Montgomery, R. and Ratiu, T.S., 1990, Reduction, Symmetry and Phases in Mechanics, Memoirs of the AMS, Vol. 436 (Providence, RI: American Mathematical Society).
13. Marsden, J.E. and West, M., 2001, Discrete mechanics and variational integrators, Acta Numerica, 10, 357-514.
14. Dellnitz, M., Junge, O., Koon, W.S., Lekien, F., Lo, M.W., Marsden, J.E., Padberg, K., Preis, R., Ross, S. and Thiere, B., 2004, Transport in dynamical astronomy and multibody problems. Preprint.
15. Radford, J., 2003, Symmetry, reduction and swimming in a perfect fluid. PhD thesis, California Institute of Technology.
16. Kanso, E., Marsden, J.E., Rowley, C.W, and Melli-Huber, J., 2004, Locomotion of articulated bodies in a perfect fluid (submitted).
17. Maciejewski, A., 1995, Reduction, relative equilibria and potential in the two rigid bodies problem. Celestial Mechanics and Dynamical Astronomy, 63, 1-28.
18. Maciejewski, A.J., 1999, The two rigid bodies problem. Reduction and relative equilibria. In Hamiltonian Systems with Three or More Degrees of Freedom (S'Agaró, 1995), Vol. 533 of NATO Advanced Science Institutes: Series C. Mathematical and Physical Sciences, pp. 475-479 (Dordrecht: Kluwer Acadamic).
19. Goździewski, K. and Maciejewski, A.J., 1999, Unrestricted planar problem of a symmetric body and a point mass. Triangular libration points and their stability. Celestial Mechanics and Dynamical Astronomy, 75, 251-285.
20. Marsden, J.E. and Ratiu, T.S., 1999, Introduction to Mechanics and Symmetry, Vol. 17 of Texts in Applied Mathematics. Vol. 17; 1994. 2nd Edn., 1999 (Berlin: Springer-Verlag).
21. Bloch, A., (with the collaboration of J. Ballieul, P. Crouch, and J. E. Marsden), 2003, NonholonomicMechanics and Control, Interdisciplinary Applied Mathematics, Vol. 24 (Berlin: Springer-Verlag).
22. Cendra, H., Marsden, J.E., Pekarsky, S. and Ratiu, T. S., 2003, Reduction of Hamilton's phase space principle. Moscow Mathematical Journal (special issue in honor of V. Arnold), 3, 833-867.
23. Marsden, J.E. and Perlmutter, M., 2000, The orbit bundle picture of cotangent bundle reduction. Comptes Rendus Mathématiques. 22, 33-54.
24. Lew, A., Marsden, J.E., Ortiz, M. and West, M., 2004, Variational time integration for mechanical systems. International Journal for Numerical Methods in Engineering, 60, 153-212.
25. Astakhov, S.A., Burbanks, A.D., Wiggins, S. and Farrelly, D., 2003, Chaos-assisted capture of irregular moons. Nature, 423, 264-267.