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Nelin. Dinam., 2012, Volume 8, Number 1, Pages 57–69 (Mi nd303)  

On invariant manifolds of nonholonomic systems

V. V. Kozlov

Steklov Mathematical Institute, Russian Academy of Sciences, Gubkina st. 8, Moscow, 119991, Russia

Abstract: Invariant manifolds of equations governing the dynamics of conservative nonholonomic systems are investigated. These manifolds are assumed to be uniquely projected onto configuration space. The invariance conditions are represented in the form of generalized Lambs equations. Conditions are found under which the solutions to these equations admit a hydrodynamical description typical of Hamiltonian systems. As an illustration, nonholonomic systems on Lie groups with a left-invariant metric and left-invariant (right-invariant) constraints are considered.

Keywords: invariant manifold, Lambs equation, vortex manifold, Bernoullis theorem, Helmholtz theorem

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Document Type: Article
UDC: 532.527+531.01
MSC: 70Hxx, 37J60
Received: 27.12.2011

Citation: V. V. Kozlov, “On invariant manifolds of nonholonomic systems”, Nelin. Dinam., 8:1 (2012), 57–69

Citation in format AMSBIB
\Bibitem{Koz12}
\by V.~V.~Kozlov
\paper On invariant manifolds of nonholonomic systems
\jour Nelin. Dinam.
\yr 2012
\vol 8
\issue 1
\pages 57--69
\mathnet{http://mi.mathnet.ru/nd303}


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