On Invariant Manifolds of Nonholonomic Systems

    2012, Volume 17, Number 2, pp.  131-141

    Author(s): Kozlov V. V.

    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.
    Keywords: invariant manifold, Lamb’s equation, vortex manifold, Bernoulli’s theorem, Helmholtz’ theorem
    Citation: Kozlov V. V., On Invariant Manifolds of Nonholonomic Systems, Regular and Chaotic Dynamics, 2012, Volume 17, Number 2, pp. 131-141

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