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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2012, Volume 8, Number 1, Pages 57–69
(Mi nd303)
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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 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.
Received: 27.12.2011 Accepted: 23.01.2012
Citation:
V. V. Kozlov, “On invariant manifolds of nonholonomic systems”, Nelin. Dinam., 8:1 (2012), 57–69
Linking options:
https://www.mathnet.ru/eng/nd303 https://www.mathnet.ru/eng/nd/v8/i1/p57
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Statistics & downloads: |
Abstract page: | 437 | Full-text PDF : | 150 | References: | 70 | First page: | 1 |
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