Symmetries and Reduction in Nonholonomic Mechanics

    2015, Vol. 11, No. 4, pp.  763–823

    Author(s): Borisov A. V., Mamaev I. S.

    This paper is a review of the problem of the constructive reduction of nonholonomic systems with symmetries. The connection of reduction with the presence of the simplest tensor invariants (first integrals and symmetry fields) is shown. All theoretical constructions are illustrated by examples encountered in applications. In addition, the paper contains a short historical and critical sketch covering the contribution of various researchers to this problem.
    Keywords: reduction, symmetry, tensor invariant, first integral, symmetry group, symmetry field, nonholonomic constraint, Noether theorem
    Citation: Borisov A. V., Mamaev I. S., Symmetries and Reduction in Nonholonomic Mechanics, Rus. J. Nonlin. Dyn., 2015, Vol. 11, No. 4, pp.  763–823

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