Geometry and integrability of Euler-Poincaré-Suslov equations

Nonlinearity

Volumn 14, Issue 6, 2001, Pages 1555-1567

  Jovanović, Božidar ^a,b  

^a UNIVERSITY OF MUNICH   (Germany)

^b MATHEMATICAL INSTITUTE   (Serbia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035511557     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/14/6/308     Document Type: Article

References (33)

1. Arnold V I, Kozlov V V and Neishtadt A I 1987 Mathematical Aspects of Classical and Celestial Mechanics, Dynamical Systems vol III (Berlin: Springer)
2. Bazaikin Ya V 2000 Double quotients of Lie groups with an integrable geodesic flows Sibirsk. Mat. Zh. 41 513-30 (in Russian) (Engl. transl. Siberian Math. J.)
3. Bazaikin Ya V 2000 Double quotients of Lie groups with an integrable geodesic flows Sibirsk. Mat. Zh. 41 513-30 (in Russian) (Engl. transl. Siberian Math. J.)
4. Bloch A M, Krishnaprasad P S, Marsden J E and Murray R M 1996 Nonholonomical mechanical systems with symmetry Arch. Rational Mech. Anal. 136 21-99
5. Bogoyavlenki O I 1983 Integrable Euler equations associated with filtrations of Lie algebras Mat. Sb. 121 233-42 (in Russian) Engl. transl. 1984 Math. USSR-Sb 49 229-38
6. Bogoyavlenki O I 1983 Integrable Euler equations associated with filtrations of Lie algebras Mat. Sb. 121 233-42 (in Russian) Engl. transl. 1984 Math. USSR-Sb 49 229-38
7. Bolsinov A V and Jovanović B 2001 Integrable geodesic flows on homogeneous spaces Mat. Sb. (in Russian) to appear (Engl. transl. Sb. Math.)
8. Bolsinov A V and Jovanović B 2001 Integrable geodesic flows on homogeneous spaces Mat. Sb. (in Russian) to appear (Engl. transl. Sb. Math.)
9. Cantrijn F, de Leon M and Martin de Diego D 1999 On almost-Poisson structures in nonholonomic mechanics Nonlinearity 12 721-37
10. Chaplygin S A 1981 Selected Works (Moscow: Nauka) (in Russian)
11. Fedorov Yu N and Kozlov V V 1995 Various aspects of n-dimensional rigid body dynamic Trans. Am. Math. Soc. Ser. 2 168 141-71
12. Hermans J 1995 A symmetric sphere rolling on a surface Nonlinearity 8 493-515
13. Jovanović B 1998 Non-holonomic geodesic flows on Lie groups and the integrable Suslov problem on S O (4) J. Phys. A: Math. Gen. 31 1415-22
14. Koiller J 1992 Reduction of some classical non-holonomic systems with symmetry Arch. Rational Mech. 118 113-48
15. Kozlov V V 1988 Invariant measures of the Euler-Poincaré equations on Lie algebras Funkt. Anal. Prilozh. 22 69-70 (in Russian) (Engl. transi. 1988 Funct. Anal. Appl. 22 58-9)
16. Kozlov V V 1988 Invariant measures of the Euler-Poincaré equations on Lie algebras Funkt. Anal. Prilozh. 22 69-70 (in Russian) (Engl. transl. 1988 Funct. Anal. Appl. 22 58-9)
17. Marle C M 1995 Reduction of constrained mechanical systems and stability of relative equilibria Commun. Math. Phys. 174 295-318
18. Mikityuk I V 1984 Integrability of the Euler equations associated with filtrations of semisimple Lie algebras Matem. Sbornik 125 167 (in Russian) (Engl. transl. 1986 Math. USSR Sbornik 53 541-9)
19. Mikityuk I V 1984 Integrability of the Euler equations associated with filtrations of semisimple Lie algebras Matem. Sbornik 125 167 (in Russian) (Engl. transl. 1986 Math. USSR Sbornik 53 541-9)
20. Mishchenko A S and Fomenko A T 1978 Generalized Liouville method of integration of Hamiltonian systems Funkts. Anal. Prilozh. 12 46-56 (in Russian) (Engl. transl. 1978 Funct. Anal. Appl. 12 113-21)
21. Mishchenko A S and Fomenko A T 1978 Generalized Liouville method of integration of Hamiltonian systems Funkts. Anal. Prilozh. 12 46-56 (in Russian) (Engl. transl. 1978 Funct. Anal. Appl. 12 113-21)
22. Paternain G P and Spatzier R J 1994 New examples of manifolds with completely integrable geodesic flows Adv. Math. 108 346-66
23. Strichartz R S 1986 Sub-Riemannian geometry J. Diff. Geom. 24 221-63 Strichartz R S 1989 J. Diff. Geom. 30 595-6
24. Strichartz R S 1986 Sub-Riemannian geometry J. Diff. Geom. 24 221-63 Strichartz R S 1989 J. Diff. Geom. 30 595-6
25. Suslov G 1951 Theoretical Mechanics (Moscow: Gostekhizdat) (in Russian)
26. Taimanov I A 1997 Integrable geodesic flows of nonholonomic metric J. Dynam. Control Syst. 3 129-47
27. Thimm A 1981 Integrable geodesic flows on homogeneous spaces Ergod. Theor. Dynam. Syst. 1 495-517
28. Trofimov V V and Fomenko A T 1994 Geometric and algebraic mechanisms of the integrability of Hamiltonian systems on homogeneous spaces and Lie algebras Dynamical Systems vol VII (Berlin: Springer)
29. Veselov A P and Veselova L E 1986 Flows on Lie groups with nonholonomic constraint and integrable non-Hamiltonian systems Funkt. Anal. Prilozh. 20 65-6 (in Russian) (Engl. transl. 1986 Funct. Anal. Appl. 20 308-9)
30. Veselov A P and Veselova L E 1986 Flows on Lie groups with nonholonomic constraint and integrable non-Hamiltonian systems Funkt. Anal. Prilozh. 20 65-6 (in Russian) (Engl. transl. 1986 Funct. Anal. Appl. 20 308-9)
31. Zenkov DV 1995 The geometry of the Routh problem J. Nonlinear Sci. 5 503-19
32. Zenkov D V and Bloch A M 2000 Dynamics of the n-dimensional Suslov problem J. Geom. Phys. 34 121-36
33. Zenkov D V and Bloch A M 2001 Dynamics of generalized Euler tops with constraints Discrete Continuous Dynam. Syst. (special issue) 398-405