Lie group variational integrators for the full body problem

Computer Methods in Applied Mechanics and Engineering

Volumn 196, Issue 29-30, 2007, Pages 2907-2924

  Lee, Taeyoung ^a   Leok, Melvin ^b   McClamroch, N Harris ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

^b PURDUE UNIVERSITY   (United States)

Author keywords

Full body problem; Lie group method; Variational integrators

Indexed keywords

HAMILTONIANS; LAGRANGE MULTIPLIERS; MATHEMATICAL MODELS; VARIATIONAL TECHNIQUES;

FULL BODY PROBLEM; LIE GROUP METHOD; VARIATIONAL INTEGRATORS;

EQUATIONS OF MOTION;

EQUATIONS OF MOTION; HAMILTONIANS; LAGRANGE MULTIPLIERS; MATHEMATICAL MODELS; VARIATIONAL TECHNIQUES;

EID: 34247559618     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2007.01.017     Document Type: Article

References (26)

1. W.S. Koon, J.E. Marsden, S. Ross, M. Lo, D.J. Scheeres, Geometric mechanics and the dynamics of asteroid pairs, in: New Trends in Astrodynamics Conference, 2003.
2. Maciejewski A.J. Reduction, relative equilibria and potential in the two rigid bodies problem. Celest. Mech. Dynam. Astron. 63 (1995) 1-28
3. Scheeres D.J. Stability in the full two-body problem. Celest. Mech. Dynam. Astron. 83 (2002) 155-169
4. D.J. Scheeres, Stability of relative equilibria in the full two-body problem, in: New Trends in Astrodynamics Conference, 2003.
5. 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 296 (2002) 1445-1448
6. D.J. Scheeres, S. Augenstein, Spacecraft motion about binary asteroids, in: Astrodynamics Specialist Conferences, 2003.
7. F. Gabern, W.S. Koon, J.E. Marsden, Spacecraft dynamics near a binary asteroid, in: Proceedings of the Fifth International Conference on Dynamical Systems and Differential Equations, 2004.
8. Scheeres D.J., and Bellerose J. The restricted hill full 4-body problem: application to spacecraft motion about binary asteroids. Dynam. Syst.: Int. J. 20 1 (2005) 23-44
9. Hairer E., Lubich C., and Wanner G. Geometric Numerical Integration (2000), Springer
10. Marsden J.E., and West M. Discrete mechanics and variational integrators. Acta Numer. 10 (2001) 357-514
11. Hairer E. Backward analysis of numerical integrators and symplectic methods. Ann. Numer. Math. 1 1-4 (1994) 107-132 scientific computation and differential equations (Auckland, 1993)
12. Iserles A., Munthe-Kaas H.Z., Nørsett S.P., and Zanna A. Lie-group methods. Acta Numer. 9 (2000) 215-365
13. Moser J., and Veselov A.P. Discrete versions of some classical integrable systems and factorization of matrix polynomials. Commun. Math. Phys. 139 (1991) 217-243
14. Wendlandt J.M., and Marsden J.E. Mechanical integrator derived from a discrete variational principle. Physica D 106 (1997) 223-246
15. Simo J.C., Tarnow N., and Wong K.K. Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics. Comput. Methods Appl. Mech. Engrg. 100 (1992) 63-116
16. Krysl P. Explicit momentum-conserving integrator for dynamics of rigid bodies approximating the midpoint Lie algorithm. Int. J. Numer. Methods Engrg. 63 15 (2005) 2171-2193
17. T. Lee, M. Leok, N.H. McClamroch, A Lie group variational integrator for the attitude dynamics of a rigid body with applications to the 3D pendulum, in: Proceedings of the IEEE Conference on Control Applications, 2005, pp. 962-967.
18. Marsden J.E., Pekarsky S., and Shkoller S. Discrete Euler-Poincaré and Lie-Poisson equations. Nonlinearity 12 (1999) 1647-1662
19. Marsden J.E., Pekarsky S., and Shkoller S. Symmetry reduction of discrete Lagrangian mechanics on Lie groups. J. Geometry Phys. 36 (2000) 139-150
20. A.K. Sanyal, J. Shen, N.H. McClamroch, Variational integrators for mechanical systems with configuration dependent inertia, Numer. Methods Engrg., submitted for publication.
21. M. Leok, Foundations of Computational Geometric Mechanics, Ph.D. thesis, California Institute of Technology, 2004.
22. Jalnapurkar S.M., Leok M., Marsden J.E., and West M. Discrete Routh reduction. J. Phys. A: Math. General 39 (2006) 5521-5544
23. Marsden J.E., and Ratiu T.S. Introduction to Mechanics and Symmetry (1999), Springer
24. Cendra H., Marsden J.E., and Ratiu T.S. Lagrangian reduction by stages. Memoirs of the American Mathematical Society 152 722 (2001)
25. Yoshida H. Construction of high order symplectic integrators. Phys. Lett. A 150 (1990) 262-268
26. T. Lee, M. Leok, N.H. McClamroch, Lie group variational integrators for the full body problem in orbital mechanics, Celest. Mech. Dynam. Astron., in press, doi:10.1007/S10569-007-9073-X.