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On invariant manifolds of nonholonomic systems. (English) Zbl 1323.70074
Summary: 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.

MSC:
70F25 Nonholonomic systems related to the dynamics of a system of particles
37J15 Symmetries, invariants, invariant manifolds, momentum maps, reduction (MSC2010)
37J60 Nonholonomic dynamical systems
37N05 Dynamical systems in classical and celestial mechanics
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