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This article is cited in 6 scientific papers (total in 6 papers)
On Invariant Manifolds of Nonholonomic Systems
Valery V. Kozlov V.A. Steklov Mathematical Institute, Russian Academy of Sciences,
ul. Gubkina 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:
Valery V. Kozlov, “On Invariant Manifolds of Nonholonomic Systems”, Regul. Chaotic Dyn., 17:2 (2012), 131–141
Linking options:
https://www.mathnet.ru/eng/rcd266 https://www.mathnet.ru/eng/rcd/v17/i2/p131
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Abstract page: | 193 |
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