Discrete nonholonomic LL systems on Lie groups

Nonlinearity

Volumn 18, Issue 5, 2005, Pages 2211-2241

  Fedorov, Yuri N ^a   Zenkov, Dmitry V ^b  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

^b NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 23444455474     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/18/5/017     Document Type: Article

References (29)

1. Arnold V I, Kozlov V V and Neishtadt A I 1989 Mathematical aspects of classical and celestial mechanics Dynamical System III (New York: Springer)
2. Bloch A M 2003 Nonholonomic Mechanics and Control (Interdisciplinary Applied Mathematics vol 24) (New York: Springer)
3. Bloch A M, Krishnaprasad P S, Marsden J E and Murray R 1996 Nonholonomic mechanical systems with symmetry Arch. Ration. Mech. Anal. 136 21-99
4. Bobenko A I and Suris Y B 1999 Discrete Lagrangian reduction, discrete Euler-Poincaré equations, and semidirect products Lett. Math. Phys. 49 79-93
5. Chaplygin S A 1911 On the theory of motion of nonholonomic systems. The theorem on the reducing multiplier Math. Sbornik XXVIII 303-14 (in Russian)
6. Cortés J and Martínez S 2001 Nonholonomic integrators Nonlinearity 14 1365-92
7. Fedorov Yu N and Kozlov V V 1995 Various aspects of n-dimensional rigid body dynamics Am. Math. Soc. Transl. 168 141-71
8. Fedorov Yu N and Zenkov D V 2005 Dynamics of the discrete Chaplygin sleigh Discrete Continuous Dyn. Syst. at press
9. Gray A 1997 Modern Differential Geometry of Curves and Surfaces with Mathematica 2nd edn (Boca Raton, FL: CRC Press)
10. Jovanović B 2001 Geometry and integrability of Euler-Poincaré-Suslov equations Nonlinearity 14 1555-657
11. Helgason S 1962 Differential Geometry and Symmetric Spaces (New York: Academic)
12. Kozlov V V 1985 On the integration theory of equations of nonholonomic mechanics Adv. Mech. 8 85-107 (in Russian)
13. Kozlov V V 1988 Invariant measures of the Euler-Poincaré equations on Lie algebras Funct. Anal. Appl. 22 58-9
14. de León M, Martín de Diego D and Santamaría Merino A 2002 Geometric integrators and nonholonomic mechanics Preprint math-ph/0211028
15. McLachlan R 1993 Explicit Lie-Poisson integration and the Euler equations Phys. Rev. Lett. 71 3043-6
16. Marsden J E, Pekarsky S and Shkoller S 1999 Discrete Euler- Poincaré and Lie-Poisson equations Nonlinearity 12 1647-62
17. Marsden J E and Ratiu T S 1999 Introduction to Mechanics and Symmetry (Texts in Applied Mathematics vol 17) (Berlin: Springer)
18. Marsden J E and West M 2001 Discrete mechanics and variational integrators Acta Numer. 10 357-514
19. Moser J and Veselov A 1991 Discrete versions of some classical integrable systems and factorization of matrix polynomials Commun. Math. Phys. 139 217-43
20. Neimark Ju I and Fufaev N A 1972 Dynamics of Nonholonomic Systems (Translations of Mathematical Monographs vol 33) (Providence, RI: American Mathematical Society)
21. Steiner's Roman Surface http://mathworld.wolfram.com/romansurface.html
22. Suslov G 1902 Theoretical Mechanics vol 2 (Kiev) (in Russian)
23. Veselov A P 1988 Integrable discrete-time systems and difference operators Funct. Anal. Appl. 22 1-13
24. Veselov A P 1991 Integrable Lagrangian correspondences and the factorization of matrix polynomials Funct. Anal. Appl. 25 38-49
25. Wendland J M and Marsden J E 1997 Mechanical integrators derived from a discrete variational principle Physica D 106 223-46
26. Whittaker E T 1960 A Treatise on Analytical Dynamics 4th edn (Cambridge: Cambridge University Press)
27. Zenkov D V and Bloch A M 2000 Dynamics of the n -dimensional Suslov problem J. Geom. Phys. 34 121-36
28. Zenkov D V and Bloch A M 2003 Invariant measures of nonholonomic flows with internal degrees of freedom Nonlinearity 16 1793-807
29. Zenkov D V 2003 Linear conservation laws of nonholonomic systems with symmetry Discrete Continuous Dyn. Syst. 963-72 (extended volume)