Bozidar Jovanovic 2001 Nonlinearity 14 1555 doi:10.1088/0951-7715/14/6/308
Geometry and integrability of Euler-Poincaré-Suslov equations
Bozidar Jovanovic1
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We consider non-holonomic geodesic flows of left-invariant metrics and left-invariant non-integrable distributions on compact connected Lie groups. The equations of geodesic flows are reduced to the Euler-Poincaré-Suslov equations on the corresponding Lie algebras. The Poisson and symplectic structures give rise to various algebraic constructions of the integrable Hamiltonian systems. On the other hand, non-holonomic systems are not Hamiltonian and the integration methods for non-holonomic systems are much less developed. In this paper, using chains of subalgebras, we give constructions that lead to a large set of first integrals and to integrable cases of the Euler-Poincaré-Suslov equations. Furthermore, we give examples of non-holonomic geodesic flows that can be seen as a restriction of integrable sub-Riemannian geodesic flows.
- PACS
- MSC
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70H06 Completely integrable systems and methods of integration
37J60 Nonholonomic dynamical systems (See also 70F25)
37J35 Completely integrable systems, topological structure of phase space, integration methods
- Subjects
- Dates
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Issue 6 (November 2001)
Received 8 February 2001
Published 18 September 2001
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Geometry and integrability of Euler-Poincaré-Suslov equations
Bozidar Jovanovic 2001 Nonlinearity 14 1555
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