Regular and Chaotic Dynamics

, Volume 17, Issue 2, pp 131–141 | Cite as

On invariant manifolds of nonholonomic systems

  • Valery V. Kozlov


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 Lamb’s 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.


invariant manifold Lamb’s equation vortex manifold Bernoulli’s theorem Helmholtz’ theorem 

MSC2010 numbers

70Hxx 37J60 


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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.V.A. Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia

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