Regular and Chaotic Dynamics

, Volume 20, Issue 5, pp 553–604 | Cite as

Symmetries and reduction in nonholonomic mechanics

  • Alexey V. BorisovEmail author
  • Ivan S. Mamaev


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.


reduction symmetry tensor invariant first integral symmetry group symmetry field nonholonomic constraint Noether theorem 

MSC2010 numbers

37J60 37J35 37C10 


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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Udmurt State UniversityIzhevskRussia
  2. 2.M. T. Kalashnikov Izhevsk State Technical UniversityIzhevskRussia

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