On invariant manifolds of nonholonomic systems
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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.
Keywordsinvariant manifold Lamb’s equation vortex manifold Bernoulli’s theorem Helmholtz’ theorem
MSC2010 numbers70Hxx 37J60
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- 1.Arzhanykh, I. S., Momentum Fields, Tashkent: Nauka, 1965 (Russian).Google Scholar
- 3.Kozlov, V.V., On Invariant Manifolds of Hamilton’s Equations, J. Appl. Math. Mech., 2012, in press. (Russian).Google Scholar
- 9.Fedorov, Yu.N. and Kozlov, V.V., Various Aspects of N-dimensional Rigid Body Dynamics, Dynamical Systems in Classical Mechanics, Amer. Math. Soc. Transl. Ser. 2, vol. 168, Providence, RI: AMS, 1995, pp. 141–171.Google Scholar
- 10.Suslov, G. K., Theoretical Mechanics, Moscow-Leningrad: Gostekhizdat, 1951 (Russian).Google Scholar