Regular and Chaotic Dynamics

, Volume 21, Issue 4, pp 455–476 | Cite as

Historical and critical review of the development of nonholonomic mechanics: the classical period

  • Alexey V. Borisov
  • Ivan S. Mamaev
  • Ivan A. Bizyaev
Article

Abstract

In this historical review we describe in detail the main stages of the development of nonholonomic mechanics starting from the work of Earnshaw and Ferrers to the monograph of Yu. I.Neimark and N.A. Fufaev. In the appendix to this review we discuss the d’Alembert–Lagrange principle in nonholonomic mechanics and permutation relations.

Keywords

nonholonomic mechanics nonholonomic constraint d’Alembert–Lagrange principle permutation relations 

MSC2010 numbers

37J60 01A05 

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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  • Alexey V. Borisov
    • 1
  • Ivan S. Mamaev
    • 2
  • Ivan A. Bizyaev
    • 3
  1. 1.Moscow Institute of Physics and TechnologyDolgoprudnyiRussia
  2. 2.Izhevsk State Technical UniversityIzhevskRussia
  3. 3.Udmurt State UniversityIzhevskRussia

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