The dynamics of Chaplygin ball: The qualitative and computer analysis

Regular and Chaotic Dynamics

Volumn 6, Issue 3, 2001, Pages 291-306

  Kilin, A A ^a  

^a UDMURT STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0013272552     PISSN: 15603547     EISSN: 14684845     Source Type: Journal    
DOI: 10.1070/RD2001v006n03ABEH000178     Document Type: Review

References (12)

1. D. K. Bobylev. On a ball with a gyroscope inside rolling without sliding on the horizontal plane. Mat. Sbornik. 1892. V. XVI. (In Russian)
2. A. V. Borisov, I. S. Mamaev. Poisson structures and algebras Lie in hamiltonian mechanics. Izhevsk, NIC RCD. 1999. P. 464. (In Russian)
3. A. V. Borisov, I. S. Mamaev. Poisson structure of the problem of Chaplygin ball rolling. Mat. zametki (to be published). (In Russian)
4. N. E. Zhukovsky. On gyroscopic ball of D. K. Bobylev. Trudy otd. fizich. nauk Obsch. lyub. estestvoznaniya. 1893. V. VI. No. 1. P. 11-17. (In Russian)
5. S. L. Ziglin. Separatrix splitting, solution branching and non existence of the integral in rigid body dynamics. Trudy Mosk. Mat. Obschestva. 1980. V. 41. P. 287-303. (In Russian)
6. V. V. Kozlov. On the theory of integration of nonholonomic mechanics equations. Advances in Mechanics. 1985. V. 8. No. 3. P. 85-107. (In Russian)
7. A. P. Markeev. On integrability of the problem of rolling of the ball with multilinked cavity filled with ideal fluid. Izv. Akad. Nauk SSSR, Ser. Mekh. tverdogo tela. 1985. No. 1. P. 64-65. (In Russian)
8. Yu. I. Neǐmark, N. A. Fufaev. Dynaics of nonholonomics systems. M.: Nauka. 1967. P. 520. (In Russian)
9. Yu. N. Fedorov. The explicit integration and isomorphisms of some problems of classical mechanics. An abstract of the dissertation for the academic degree of candidate of physical and mathematical sciences. M.: MGU. 1989. (In Russian)
10. S. A. Chaplygin. On the motion of a heavy rigid body of rotation on a plane. Collection of papers. V. 1. M.-L.: GITTL. 1948. P. 57-75. (In Russian)
11. S. A. Chaplygin. On a ball rolling on the horizontal plane. Collection of papers. V. 1. M.-L.: GITTL. 1948. P. 76-101. (In Russian)
12. V. Volterra. Sur la theorie des variations des latitudes. Acta Math. 1899. V. 22. P. 201-358.