Poisson structures for reduced non-holonomic systems

Journal of Physics A: Mathematical and General

Volumn 37, Issue 17, 2004, Pages 4821-4842

  Ramos, Arturo ^a  

^a UNIVERSITY OF PADOVA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2442515072     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/37/17/012     Document Type: Article

References (43)

1. Bates L 1998 Rep. Math. Phys. 42 231-47
2. Bates L 2002 Rep. Math. Phys. 49 143-9
3. Bates L and Cushman R 1999 Rep. Math. Phys. 44 29-35
4. Bates L, Graumann H and MacDonnell C 1996 Rep. Math. Phys. 37 295-308
5. Bates L and Śniatycki J 1992 Rep. Math. Phys. 32 99-115
6. Bloch A M, Krishnaprasad P S, Marsden J E and Murray R M 1996 Arch. Ration. Mech. Anal. 136 21-99
7. Borisov A V and Mamaev I S 2002 Regular Chaotic Dyn. 7 177-200
8. Borisov A V, Mamaev I S and Kilin A A 2002 Regular Chaotic Dyn. 7 201-19
9. Cantrijn F, Cortés J, de León M and Martín de Diego D 2002 Math. Proc. Camb. Phil. Soc. 132 323-51
10. Cantrijn F, de León M, Marrero J C and Martín de Diego D 1998 Rep. Math. Phys. 42 25-45
11. Cantrijn F, de León M and Martín de Diego D 1999 Nonlinearity 12 721-37
12. Cardin F and Favretti M 1996 J. Geom. Phys. 18 295-325
13. Cariñena J F, Ibort L A, Marmo G and Perelomov A 1994 J. Phys. A: Math. Gen. 27 7425-49
14. Cariñena J F, Grabowski J and Ramos A 2001 Acta Appl. Math. 66 67-87
15. Cariñena J F and Ramos A 2002 Acta Appl. Math. 70 43-69
16. Cariñena J F and Ramos A 2003 Applications of Lie systems in quantum mechanics and control theory Classical and Quantum Integrability ed J Grabowski, G Marmo and P Urbański (Banach Center Publications vol 59) (Warszawa: Polish Academy of Sciences)
17. Cushman R 1998 Rep. Math. Phys. 42 47-70
18. Cushman R, Hermans J and Kemppainen D 1996 The rolling disc Nonlinear Dynamical Systems and Chaos ed H W Broer, S A van Gils, I Hoveijn and F Takens (Basel: Birkhäuser)
19. Cushman R, Kemppainen D, gniatycki J and Bates L 1995 Rep. Math. Phys. 36 275-86
20. Ebenfeld S and Scheck F 1995 Ann. Phys., NY 243 195-217
21. Fassò F 1998 Ergod. Th. Dyn. Syst. 18 1349-62
22. Fassò F and Giacobbe A 2002 J. Geom. Phys. 44 156-70
23. Fassò F, Giacobbe A and Sansonetto N Periodic flows, Poisson structures and nonholonomic mechanics, in preparation
24. Fedorov Yu N and Jovanović B 2003 Nonholonomic LR systems as generalized Chaplygin systems with an invariant measure and geodesic flows on homogeneous spaces Preprint math-ph/0307016
25. Hermans J 1995 Nonlinearity 8 493-515
26. Libermann P and Marle Ch-M 1987 Symplectic Geometry and Analytical Mechanics (Dordrecht: Reidel)
27. Lichnerowicz A 1977 J. Diff. Geom. 12 253-300
28. Marle Ch-M 1995 Commun. Math. Phys. 174 295-318
29. Marle Ch-M 1996 Rend. Sem. Mat. Univ. Pol. Torino 54 353-64
30. Marle Ch-M 1997 J. Geom. Phys. 23 350-9
31. Marle Ch-M 1998 Rep. Math. Phys. 42 211-29
32. Marle Ch-M 2003 On symmetries and constants of motion in Hamiltonian systems with nonholonomic constraints Classical and Quantum Integrability ed J Grabowski, G Marmo and P Urbański (Banach Center Publications vol 59) (Warszawa: Polish Academy of Sciences)
33. Neǐmark J I and Fufaev N A 1972 Dynamics on Nonholonomic Systems (Providence, RI: American Mathematical Society)
34. Nijenhuis A 1955 Indag. Math. 17 390-403
35. Routh E J 1955 Advanced Part of a Treatise on the Dynamics of a System of Rigid Bodies, reprint, (New York: Dover)
36. van der Schaft A J and Maschke B M 1994 Rep. Math. Phys. 34 225-33
37. Schouten J A 1954 On the differential operators of first order in tensor calculus Convegno Internazionale di Geometria Differenziale (Italia, 20-26 Settembre 1953) (Roma: Edizioni Cremonese della Casa Editrice Perrella)
38. Śniatycki J 1998 Rep. Math. Phys. 42 5-23
39. Śniatycki J 2001 Rep. Math. Phys. 48 235-48
40. Śniatycki J 2002 Rep. Math. Phys. 49 371-94
41. Weinstein A 1983 J. Diff. Geom. 18 523-57
42. Zenkov D V 1995 J. Nonlinear Sci. 5 503-19
43. Zenkov D V and Bloch A M 2003 Nonlinearity 16 1793-807