Discrete Euler-Poincaré and Lie-Poisson equations

Nonlinearity

Volumn 12, Issue 6, 1999, Pages 1647-1662

  Marsden, Jerrold E ^a   Pekarsky, Sergey ^a   Shkoller, Steve ^b  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033228880     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/12/6/314     Document Type: Article

References (15)

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4. [CMR 98] Cendra H, Marsden J E and Ratiu T S 1998 Lagrangian reduction by stages
5. [CS 91] Channell P J and Scovel J C 1991 Integrators for Lie-Poisson dynamical systems Physica D 50 80-88
6. [DF 76] Dragt A J and Finn J M 1976 Lie series and invariant functions for analytic symplectic maps J. Math. Phys. 17 2215-27
7. [GM 88] Ge Z and Marsden J E 1988 Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators Phys. Lett. A 133 134-9
8. [K 66] Kostant B 1966 Orbits, symplectic structures and representation theory Proc. US-Japan Seminar on Diff. Geom. (Kyoto, 1965) (Tokyo: Nippon Hyronsha)
9. [LS 96] Lewis D and Simo J C 1996 Conserving algorithms for the N-dimensional rigid body Fields Inst. Commun. 10 121-39
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11. [MR 94] Marsden J E and Ratiu T S 1999 Introduction to Mechanics and Symmetry 2nd edn (Berlin: Springer)
12. [Mc 93] McLachlan R 1993 Explicit Lie-Poisson entegration and the euler equations Phys. Rev. Lett. 71 3043-6
13. [McS 96] McLachlan R and Scovel C 1996 A survey of open problems in symplectic integration Fields Inst. Commun. 10 151-80
14. [MoV 91] Moser J and Veselov A P 1991 Discrete versions of some classical integrable systems and factorization of matrix polynomials Commun. Math. Phys. 139 217-43
15. [WM 97] Wendlandt J M and Marsden J E 1997 Mechanical integrators derived from a discrete variational principle Physica D 106 223-46