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Theoretical and Applied Mechanics, 2020, Volume 47, Issue 2, Pages 155–168
DOI: https://doi.org/10.2298/TAM200120009B (Mi tam83) 		 
This article is cited in 5 scientific papers (total in 5 papers)

On rheonomic nonholonomic deformations of the Euler equations proposed by Bilimovich

A. V. Borisov, A. V. Tsiganov

Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
Full-text PDF (711 kB) Citations (5)
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DOI: https://doi.org/10.2298/TAM200120009B
Abstract: In 1913 A. D. Bilimovich observed that rheonomic constraints which are linear and homogeneous in generalized velocities are ideal. As a typical example, he considered rheonomic nonholonomic deformation of the Euler equations whose scleronomic version is equivalent to the nonholonomic Suslov system. For the Bilimovithch system, equations of motion are reduced to quadrature, which is discussed in rheonomic and scleronomic cases.
Keywords: rheonomic Lagrangian systems, nonholonomic mechanics, integrability by quadratures.
Funding agency Grant number
Russian Science Foundation 19-71-30012
This work was supported by the Russian Science Foundation (project no. 19-71-30012) and performed at the Steklov Mathematical Institute of the Russian Academy of Sciences.
Received: 20.01.2020
Revised: 25.06.2020
Bibliographic databases:
Document Type: Article
MSC: 37J60, 70F25
Language: English
Citation: A. V. Borisov, A. V. Tsiganov, “On rheonomic nonholonomic deformations of the Euler equations proposed by Bilimovich”, Theor. Appl. Mech., 47:2 (2020), 155–168
Citation in format AMSBIB
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\pages 155--168
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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