On invariant manifolds of nonholonomic systems
V. V. Kozlov
Steklov Mathematical Institute, Russian Academy of Sciences, Gubkina st. 8, Moscow, 119991, Russia
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
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MSC: 70Hxx, 37J60
V. V. Kozlov, “On invariant manifolds of nonholonomic systems”, Nelin. Dinam., 8:1 (2012), 57–69
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\paper On invariant manifolds of nonholonomic systems
\jour Nelin. Dinam.
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