Dynamics of rolling disk

Regular and Chaotic Dynamics

Volumn 8, Issue 2, 2003, Pages 201-212

  Borisov, A V ^a   Mamaev, I S ^a   Kilin, A A ^a  

^a Institute of Computer Science   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 27944441249     PISSN: 15603547     EISSN: 14684845     Source Type: Journal    
DOI: 10.1070/RD2003v008n02ABEH000237     Document Type: Article

References (28)

1. A. A. Afonin, V. V. Kozlov. Problem on falling of disk moving on horizontal plane. Proc. of Russian Acad, of Sciences, Rigid body mech. No 1. 1997. P. 7-13.
2. P. Appel. Sur l'intégration des équations du mouvement d'un corps pesant de rédolution roulant par une arête circulaire sur up plan horizontal; cas parficulier du cerceau. R.endiconti del circolo matematico di Palermo. V. 14. 1900. P. 1-6.
3. A. V. Borisov, I. S. Mamaev. Rigid body dynamics. Izhevsk: RCD publ.. 2001. P. 384.
4. A. V. Borisov, I. S. Mamaev. Poisson structures and Lie algebras in Hamiltonian mechanics. Izhevsk: RCD publ. 1999. P. 464.
5. A. V. Borisov, I. S. Mamaev. The rolling of rigid body on a plane and sphere. Hierarchy of dynamic. Regular and Chaotic Dynamics. V. 7. No1. 2002. P. 177-200.
6. S. A. Chaplygin. On motion of heavy rigid body of revolution on horizontal plane. Proc. of the Physical Sciences' section of the Society of Amateurs of Natural Sciences. V. 9. No 1. 1897. P. 10-16.
7. R. Cushman, J. Hermans, D. Kemppainen. The rolling disk. University of Calgary, Preprint. 1995. P. 51.
8. Yu. N. Fedorov. On disk rolling on absolutely rough surface. Proc. of USSR. Acad. of sciences, Rigid body mech. No 4. 1987. P. 67-75.
9. N. M. Ferrers. Extension of Lagrange's equations. Quart. J. of pure and applied Mathematics. V. 12. No45. 1872. P. 1-5.
10. E. G. Gellop. On the rise of a Spinning Top. Proc. Cambr. Phylos. Soc. V. 19, pt. 3. 1904. P. 356-373.
11. A. V. Karapetyan. Stability of stationary motions. M., "Editorial URRS". 1998. P. 168.
12. A. A. Kilin. The Dynamics of Chaplygin Ball: the Qualitative and Computer Analysis. Regular and Chaotic Dynamics. V. 6. No3. 2001. P. 291-306.
13. S. N. Kolesnikov. On rolling of disk on horizontal plane. MGU Bull. Math.& Mech. Series. No2. 1985. P. 55-60.
14. D. Korteweg. Extrait d'une lettre à M. Appel. Rendiconti del circolo matematico di Palermo. V. 14. 1900. P. 7-8.
15. V. V. Kozlov. On integration theory of nonholonomic mechanics equations. Advances of mech. V. 8. No3. 1985. P. 85-101.
16. V. V. Kozlov. Liouvillian property of invariant measures of completely integrable systems and Monzh-Ampere equation. Math, notes. V. 53. No4. 1993. P. 45-52.
17. V. V. Kozlov. Methods of qualitative analysis in rigid body dynamics. Izhevsk: RCD publ. 2000. P. 256.
18. V. V. Kozlov. On motion of disk on an inclined plain. Proc. of Russian Acad. of Sciences, Rigid body mech. No5. 1996. P. 29-35.
19. V. V. Kozlov. Symmetries, topology, and resonances in Hamiltonian mechanics. Izhevsk, Udm. State Univ. publ.. 1995.
20. V. V. Kozlov, N. N. Kolesnikov. On theorems of dynamics. Appl. Math. & Mech. V. 42. No1. 1978. P. 28-33.
21. A. S. Kuleshov. On stationary rollings of disk on rough surface. Appl. Math. & Mech. V. 65. No1. 2001. P. 173-175.
22. K. Magnus. Gyroscope: theory and applications. M.: Mir. 1974. P. 526.
23. A. P. Markeev. Dynamics of body contacting hard surface. M.: Nauka. 1992. P. 336.
24. N. K. Moschuk. Qualitative analysis of motion of heavy rigid body of rotation on absolutely rough plain. Appl. Math. & Mech. V. 52. No2. 1988. P. 203-210.
25. N. K. Moschuk. On reduction of equations of motion of some nonholonomic Chaplygin systems to Lagrangian and Hamiltonian equations. Appl. Math. & Mech. V. 51. No2. 1987. P. 223-229.
26. Yu. I. Neimark, N. A. Fufaev. Dynamics of nonholonomic systems. M.: Nauka. 1967. P. 591.
27. O. M. O 'Reilly. The dynamics of rolling disks and sliding disks. Nonlinear Dynamics. V. 10. 1996. P. 287-305.
28. G. M. Slesser. Notes on rigid dynamics. Quart. J. of mathematics. V. 4. 1861. P. 65-67.