Rolling of a symmetric sphere on a horizontal plane without sliding or spinning

Reports on Mathematical Physics

Volumn 57, Issue 3, 2006, Pages 367-374

  Cendra, Hernán ^a   Etchechoury, María ^b  

^a UNIVERSIDAD NACIONAL DEL SUR   (Argentina)

^b UNIVERSIDAD NACIONAL DE LA PLATA   (Argentina)

Author keywords

integrability; nonholonomic; symmetric rolling sphere

Indexed keywords

EID: 33747294717     PISSN: 00344877     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0034-4877(06)80027-3     Document Type: Article

References (15)

1. Neimark J.I., and Fufaev N.A. Dynamics of Nonholonomic Systems. Translations of Mathematical Monographs 33 (1972), AMS, Providence RI
2. Cendra H., Marsden J.E., and Ratiu T.S. Mathematics Unlimited and Beyond (2001), Springer, Berlin
3. Bloch A.M., Krishnaprasad P.S., Marsden J.E., and Murray R.M. Nonholonomic mechanical systems with symmetry. Arch. Rational Mech. Anal. 136 (1996) 21
4. Chaplygin S.A. On a rolling sphere on a horizontal plane. Reg. Chaotic Dyn. 7 (2002) 131
5. To appear in. Cendra H., and Díaz V. The Lagrange-d'Alembert-Poincaré equations and integrability for the rolling disk. Reg. Chaotic Dyn. (2005)
6. Cushman R. Rouths sphere. Rep. Math. Phys. 42 (1998) 47
7. Borisov A.V., Mamaev I.S., and Kilin A.A. Dynamics of rolling disk. Reg. Chaot. Dyn. 8 (2002) 201
8. Cendra H., Lacomba E.A., and Reartes W.A. The Lagrange D'Alembert-Poincaré equations for the symmetric rolling sphere. Actas del VI Congreso Antonio Monteiro (2002), Universidad Nacional del Sur, Bahia Blanca 19
9. Cortes Monforte J. Geometric, Control and Numerical Aspects of Nonholonomic Systems. Lecture Notes in Mathematics (2002), Springer, Berlin
10. Ehlers K., Koiller J., Montgomery R., and Rios P.M. The breadth of symplectic and Poisson geometry. Progr. Math. 232 (2005), Birkhäuser Boston, Boston
11. Fedorov Y.N., and Jovanovic B. Nonholonomic LR systems as generalized Chaplygin systems with an invariant measure and flows on homogeneous spaces. J. Nonlinear Sci. 14 (2004) 341
12. Borisov A.V., Mamaev I.S., and Kilin A.A. Rolling a ball on a surface. New integrals and hierachy of dynamics. Reg. Chaotic Dyn. 7 (2002) 201
13. Veselov A.P., and Veselova L.E. Integrable Nonholonomic systems on Lie groups (Russian). Mat. Zametki 44 (1988) 604
14. translation in. Veselov A.P., and Veselova L.E. Integrable Nonholonomic systems on Lie groups (Russian). Math. Notes 44 (1989) 810
15. A. V. Borisov and I. S. Mamaev: Hamiltonization of nonholonomic systems, http://xxx.Ian.gov/PS cache/nlin/pdf/0509036.pdf.