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Regular and Chaotic Dynamics, 2017, Volume 22, Issue 4, Pages 435–447
DOI: https://doi.org/10.1134/S1560354717040062 (Mi rcd264) 		 
This article is cited in 13 scientific papers (total in 13 papers)

An Inhomogeneous Chaplygin Sleigh

Alexey V. Borisov, Ivan S. Mamaev

Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
Citations (13)
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DOI: https://doi.org/10.1134/S1560354717040062
Abstract: In this paper we investigate the dynamics of a system that is a generalization of the Chaplygin sleigh to the case of an inhomogeneous nonholonomic constraint. We perform an explicit integration and a sufficiently complete qualitative analysis of the dynamics.
Keywords: Chaplygin sleigh, inhomogeneous nonholonomic constraints, conservation laws, qualitative analysis, resonance.
Funding agency Grant number
Russian Science Foundation 14-50-00005
This work was supported by the Russian Science Foundation (project 14-50-00005).
Received: 02.06.2017
Accepted: 06.07.2107
Bibliographic databases:
Document Type: Article
MSC: 37J60
Language: English
Citation: Alexey V. Borisov, Ivan S. Mamaev, “An Inhomogeneous Chaplygin Sleigh”, Regul. Chaotic Dyn., 22:4 (2017), 435–447
Citation in format AMSBIB
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\by Alexey V. Borisov, Ivan S. Mamaev
\paper An Inhomogeneous Chaplygin Sleigh
\jour Regul. Chaotic Dyn.
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\vol 22
\issue 4
\pages 435--447
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  • https://www.mathnet.ru/eng/rcd/v22/i4/p435
    Translation
    This publication is cited in the following 13 articles:
    1. Ali Ahmadi, Mahdi Gorji, Ahmad Peymaei, Kimia Khosravi Soofi, Ali Kamali, “Autonomous swimming on limit cycles with disturbance rejection capability for a fish-inspired robot”, Nonlinear Dyn, 2024  crossref
    2. Alexander A. Kilin, Elena N. Pivovarova, “Bifurcation analysis of the problem of a “rubber” ellipsoid of revolution rolling on a plane”, Nonlinear Dyn, 2024  crossref
    3. Evgeniya Mikishanina, “The problem of acceleration in the dynamics of a double-link wheeled vehicle with arbitrarily directed periodic excitation”, Theor. Appl. Mech., 50:2 (2023), 205–221  mathnet  crossref
    4. E. A. Mikishanina, “Nonholonomic mechanical systems on a plane with a variable slope”, Zhurnal SVMO, 25:4 (2023), 326–341  mathnet  mathnet  crossref
    5. Shumin Man, Qiang Gao, Wanxie Zhong, “High order symmetric algorithms for nonlinear dynamical systems with non-holonomic constraints”, Mathematics and Computers in Simulation, 212 (2023), 524  crossref
    6. Evgeniya A. Mikishanina, “Dynamics of the generalized penny-model on the rotating plane”, Eur. Phys. J. B, 96 (2023), 15–8  mathnet  crossref  isi
    7. E. M. Artemova, A. A. Kilin, Yu. V. Korobeinikova, “Issledovanie orbitalnoi ustoichivosti pryamolineinykh kachenii roller-reisera po vibriruyuschei ploskosti”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 32:4 (2022), 615–629  mathnet  crossref  mathscinet
    8. E. A. Mikishanina, “Qualitative Analysis of the Dynamics of a Trailed Wheeled Vehicle with Periodic Excitation”, Rus. J. Nonlin. Dyn., 17:4 (2021), 437–451  mathnet  crossref
    9. Alexander A. Kilin, Elena N. Pivovarova, “Qualitative Analysis of the Nonholonomic Rolling of a Rubber Wheel with Sharp Edges”, Regul. Chaotic Dyn., 24:2 (2019), 212–233  mathnet  crossref
    10. V. Fedonyuk, Ph. Tallapragada, “Sinusoidal control and limit cycle analysis of the dissipative Chaplygin sleigh”, Nonlinear Dyn., 93:2 (2018), 835–846  crossref  isi  scopus
    11. A. P. Ivanov, “On singular points of equations of mechanics”, Dokl. Math., 97:2 (2018), 167–169  mathnet  crossref  crossref  zmath  isi  elib  scopus
    12. I. A. Bizyaev, “Sani Chaplygina s dvizhuscheisya tochechnoi massoi”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:4 (2017), 583–589  mathnet  crossref  elib
    13. Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Chaplygin Sleigh with Parametric Excitation: Chaotic Dynamics and Nonholonomic Acceleration”, Regul. Chaotic Dyn., 22:8 (2017), 955–975  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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