Various approaches to conservative and nonconservative nonholonomic systems

Reports on Mathematical Physics

Volumn 42, Issue 1-2, 1998, Pages 211-229

  Marle, Charles Michel ^a  

^a INSTITUT DE MATHÉMATIQUES DE JUSSIEU   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032132873     PISSN: 00344877     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0034-4877(98)80011-6     Document Type: Article

References (48)

1. [1] P. Appell: C. R. Acad. Sc. Paris, 152 (1911), 1197-1199.
2. [2] P. Appell: Rend. Circ. Mat. Palermo 32 (1911), 48-50.
3. [3] V. I. Arnol'd, V. V. Kozlov and A. I. Neishtadt: Mathematical aspects of classical and celestial mechanics, in: Dynamical Systems III, V. I. Arnol'd (Ed.), Springer, Berlin, Heidelberg, New York 1988.
4. [4] F. Barone, R. Grassini and G. Mendella: A unified approach to constrained mechanical systems as implicit differential equations, preprint, Università di Napoli 1996.
5. [5] L. Bates and J. Śniatycki: Rep. Math. Phys. 32 (1991), 99-115.
6. [6] L. Bates, H. Graumann and C. MacDonnell: Rep. Math. Phys. 37 (1996), 295-308.
7. [7] S. Benenti: Geometrical aspects of the dynamics of non-holonomic systems, Journées relativistes, Chambéry, 14-16 May 1987.
8. [8] A. M. Bloch, P. S. Krishnaprasad, J. E. Marsden and G. Sánchez de Alvarez: Automatica 28 (1992), 745-756.
9. [9] A. Bloch, P. S. Krishnaprasad, J. E. Marsden and R. M. Murray: Arch. Ration. Mech. Anal. 136 (1996), 21-99.
10. [10] F. Cardin and M. Favretti: On nonholonomic and vakonomic dynamics of mechanical systems with nonintegrable constraints, J. Geom. Phys. 18 (1996), 295-325.
11. [11] J. F. Cariñena and M. F. Rañada: J. Phys. A: Math. Gen. 26 (1993), 1335-1351.
12. [12] N. G. Chetaev: On Gauss principle (in Russian), Izv. Kazan Fiz. Mat. Obs. 6 (1932), 323-326.
13. [13] R. Cushman, D. Kemppainen, J. Śniatycki and L. Bates: Rep. Math. Phys. 36 (1995), 275-286.
14. [14] R. Cushman, J. Hermans and D. Kemppainen: The rolling disc, Progress in nonlinear differential equations and their applications 19 (1996), 21-60.
15. [15] P. Dazord: Illinois J. Math. 38, 1 (1994), 148-175.
16. [16] E. Delassus: C. R. Acad. Sc. Paris 152 (1911), 1739-1743.
17. [17] E. Delassus: C. R. Acad. Sc. Paris 153 (1911), 626-628.
18. [18] M. de León and D. Martín de Diego: J. Math. Phys. 37, 7 (1996), 1-26.
19. [19] M. de León, M., J. C. Marrero and D. Martín de Diego: Mechanical systems with non-linear constraints, preprint, 1996.
20. [20] J. Hermans: Nonlinearity 8, 4 (1995), 493-515.
21. [21] J. Hermans: Rolling rigid bodies with and without symmetries, Ph.D. thesis, University of Utrecht, 1995.
22. [22] A. Ibort, M. de León, G. Marmo and D. Martín de Diego: Non-holonomic constrained systems as implicit differential equations, to appear in the Proceedings of the Workshop on Geometry and Physics in honour of W. Tulczyjew, Vietri, Italy, September 29 - October 3, 1996.
23. [23] J. Koiller: Arch. Ration. Mech. Anal. 118 (1992), 133-148.
24. [24] W.-S. Koon and J. E. Marsden: SIAM J. Control Optim. 35 (1997), 901-929.
25. [25] W.-S. Koon and J. E. Marsden: Poisson reduction for nonholonomic mechanical systems with symmetry, Preprint of the California Institute of Technology, 1997.
26. [26] D. J. Korteweg: Über eine ziemlich verbreitete unrichtige Behandlungssweise eines Problemes der rollenden Bewegung, über die Theorie dieser Bewegung, und insbesondere über kleine Rollende Schwingungen um eine Gleichgewichtslage, Nieu Archief voor Wiskunde, 4 (1899), 130-155.
27. [27] A. D. Lewis and R. M. Murray: Int. J. Non-Linear Mechanics, 30 (1995), 793-815.
28. [28] A. D. Lewis: Rep. Math. Phys. 38 (1996), 11-28.
29. [29] A. Lichnerowicz: J. Differential Geometry 12 (1977), 253-300.
30. [30] C-M. Marle: Commun. Math. Phys. 174 (1995), 295-318.
31. [31] C.-M. Marle: Kinematic and geometric constraints, servomechanisms and control of mechanical systems, to appear in the Proceedings of the Workshop on Geometry and Physics in honour of W. Tulczyjew, Vietri, Italy, September 29 - October 3, 1996.
32. [32] G. Marmo, G. Mendella and W. M. Tulczyjew: Constrained Hamiltonian systems as implicit differential equations, preprint, 1996.
33. [33] E. Massa and E. Pagani: Ann. Inst. Henri Poincaré, Physique théorique 55, 1 (1991), 511-544.
34. [34] E. Massa and E. Pagani: Ann. Inst. Henri Poincaré, Physique théorique 66, 1 (1997), 1-36.
35. [35] Y. Pironneau: Sur les liaisons non holonomes non linéaires, déplacements virtuels à travail nul, conditions de Chetaev, Proceedings of the IUTAM-ISIMM Symposium on Modern Developments in Analytical Mechanics, vol. II. Torino, June 7-11, 1982. Accademia delle Scienze di Torino, Torino 1983, 671-686.
36. [36] W. Sarlet, F. Cantrijn and D. J. Saunders: J. Phys. A: Math. Gen. 28, (1995), 3253-3268.
37. [37] W. M. Tulczyjew: C. R. Acad. Sc. Paris 280, A (1975), 1295-1298.
38. [38] W. M. Tulczyjew: Ann. Inst. Henri Poincaré 27 (1977), 101-114.
39. [39] W. M. Tulczyjew: Geometric formulations of physical theories, Bibliopolis, Napoli, Italy (1989).
40. [40] A. J. Van der Schaft and B. M. Maschke: Rep. Math. Phys. 34 (1994), 225-233.
41. [41] A. M. Vershik: Classical and non-classical dynamics with constraints, in: Global Analysis, Studies and Applications 1, Yu. G. Borisovich and Yu. E. Gliklikh (Ed.), 278-301. Lecture Notes in Mathematics 1108, Springer, Berlin 1984.
42. [42] A. M. Vershik and L. D. Faddeev: Sel. Math. Sov. 1 (1981), 339-350.
43. [43] A. M. Vershik and T. Ya. Gershkovich: Nonholonomic dynamical systems, geometry of distributions and variational problems, in Dynamical Systems VII, V. I. Arnold and S. P. Novikov (Eds.), 1-81, Springer, Berlin 1994.
44. [44] R. W. Weber: Arch. Ration. Mech. Anal. 92 (1985), 309-335.
45. [45] A. Weinstein: J. Differential Geometry 18 (1983), 523-557 and 22 (1985), 255.
46. [45] A. Weinstein: J. Differential Geometry 18 (1983), 523-557 and 22 (1985), 255.
47. [46] E. T. Whittaker: A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, Cambridge University Press, (1904). Fourth edition (1937), reissued with Foreword (1988).
48. [47] D. V. Zenkov: J. Nonlinear Sci. 5 (1995), 503-519.