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Extended Abstracts Spring 2018 pp 1–6Cite as

Birkhäuser

Constructive Method of Decomposition in Singularly Perturbed Problems of Non-holonomic Mechanics

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Part of the book series: Trends in Mathematics ((RPCRMB,volume 11))

Abstract

The method of decomposition of singularly perturbed differential systems is developed and application of the method to the problems of non-holonomic mechanics is considered.

A. Kobrin was funded by the Russian Foundation for Basic Research (grant 16-01-00429). V. Sobolev was supported by the Russian Foundation for Basic Research and the Government of the Samara Region (grant 16-41-630524-p) and the Ministry of Education and Science of the Russian Federation under the Competitiveness Enhancement Programme of Samara University (2013–2020).

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References

  1. S.A. Chaplygin, On the theory of motion of nonholonomic systems. The reducing multiplier theorem. Math. Collection. 28(1911), 303–314

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  2. J. Eldering, Realizing nonholonomic dynamics as limit of friction forces. Regul. Chaotic Dyn. 21, 390–409 (2016)

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  3. A. Kobrin, V. Sobolev, Integral manifolds of fast-slow systems in nonholonomic mechanics. J. Proc. Eng. 201, 556–560 (2017)

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  4. S. Koshkin, V. Jovanovic, Realization of non-holonomic constrains and singular perturbation theory for plane dumbbels. J. Eng. Math. 1, 1–19 (2017)

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  5. V.A. Sobolev, Integral manifolds and decomposition of singularly perturbed systems. Syst. Control Lett. 5, 169–179 (1984)

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Author information

Authors and Affiliations

  1. Moscow Power Engineering Institute, Moscow, Russia

    Alexander Kobrin

  2. Department of Differential Equations and Control Theory, Samara National Research University, Moskovskoye shosse, 34, Samara, 443086, Russian Federation

    Vladimir Sobolev

Authors
  1. Alexander Kobrin
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  2. Vladimir Sobolev
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Corresponding author

Correspondence to Alexander Kobrin .

Editor information

Editors and Affiliations

  1. Centre de Recerca Matemàtica, Universitat Autònoma de Barcelona, Barcelona, Spain

    Andrei Korobeinikov

  2. Facultat de Ciències, Universitat Autònoma de Barcelona, Barcelona, Spain

    Magdalena Caubergh

  3. Departament de Matemàtiques, Universitat Politècnica de Catalunya, Barcelona, Spain

    Tomás Lázaro

  4. Centre de Recerca Matemàtica, Universitat Autònoma de Barcelona, Barcelona, Spain

    Josep Sardanyés

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Kobrin, A., Sobolev, V. (2019). Constructive Method of Decomposition in Singularly Perturbed Problems of Non-holonomic Mechanics. In: Korobeinikov, A., Caubergh, M., Lázaro, T., Sardanyés, J. (eds) Extended Abstracts Spring 2018. Trends in Mathematics(), vol 11. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-25261-8_1

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