Alexey V. Borisov, Ivan S. Mamaev, Ivan A. Bizyaev, “Historical and Critical Review of the Development of Nonholonomic Mechanics: the Classical Period”, Regul. Chaotic Dyn., 2016, Volume 21, Issue 4,Pages <nobr>455

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Historical and Critical Review of the Development of Nonholonomic Mechanics: the Classical Period

Alexey V. Borisov^a, Ivan S. Mamaev^b, Ivan A. Bizyaev^c

^a Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, 141700 Russia
^b Izhevsk State Technical University Studencheskaya 7, Izhevsk, 426069 Russia
^c Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia

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.

MSC: 37J60, 01A05

Language: English

DOI: 10.1134/S1560354716040055