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Regular and Chaotic Dynamics, 2001, Volume 6, Issue 3, Pages 291–306
DOI: https://doi.org/10.1070/RD2001v006n03ABEH000178
(Mi rcd846)
 

This article is cited in 68 scientific papers (total in 68 papers)

The Dynamics of Chaplygin Ball: the Qualitative and Computer Analysis

A. A. Kilin

Laboratory of Dynamical Chaos and Nonlinearity, Udmurt State University, Universitetskaya, 1, 426034, Izhevsk, Russia
Citations (68)
Abstract: The motion of Chaplygin ball with and without gyroscope in the absolute space is analyzed. In particular, the trajectories of the point of contact are studied in detail. We discuss the motions in the absolute space, that correspond to the different types of motion in the moving frame of reference related to the body. The existence of the bounded trajectories of the ball's motion is shown by means of numerical methods in the case when the problem is reduced to a certain Hamiltonian system.
Received: 03.06.2001
Bibliographic databases:
Document Type: Article
MSC: 70E18
Language: English
Citation: A. A. Kilin, “The Dynamics of Chaplygin Ball: the Qualitative and Computer Analysis”, Regul. Chaotic Dyn., 6:3 (2001), 291–306
Citation in format AMSBIB
\Bibitem{Kil01}
\by A. A. Kilin
\paper The Dynamics of Chaplygin Ball: the Qualitative and Computer Analysis
\jour Regul. Chaotic Dyn.
\yr 2001
\vol 6
\issue 3
\pages 291--306
\mathnet{http://mi.mathnet.ru/rcd846}
\crossref{https://doi.org/10.1070/RD2001v006n03ABEH000178}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1860148}
\zmath{https://zbmath.org/?q=an:1074.70513}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2001RCD.....6..291K}
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  • https://www.mathnet.ru/eng/rcd846
  • https://www.mathnet.ru/eng/rcd/v6/i3/p291
  • This publication is cited in the following 68 articles:
    1. E. A. Mikishanina, “Two Ways to Control a Pendulum-Type Spherical Robot on a Moving Platform in a Pursuit Problem”, Mech. Solids, 59:1 (2024), 127  crossref
    2. E. A. Mikishanina, “Upravlenie kacheniem dinamicheski simmetrichnogo shara po naklonnoi vraschayuscheisya ploskosti”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 24:3 (2024), 402–414  mathnet  crossref  mathscinet
    3. E. A. Mikishanina, “Two Ways to Control a Pendulum-Type Spherical Robot on a Moving Platform in a Pursuit Problem”, Izvestiâ Rossijskoj akademii nauk. Mehanika tverdogo tela, 2024, no. 1, 230  crossref
    4. E. A. Mikishanina, “Printsipy realizatsii servosvyazei v negolonomnykh mekhanicheskikh sistemakh”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2024, no. 89, 103–118  mathnet  crossref
    5. E. A. Mikishanina, “Negolonomnye mekhanicheskie sistemy na ploskosti s peremennym uglom naklona”, Zhurnal SVMO, 25:4 (2023), 326–341  mathnet  crossref  mathscinet
    6. Evgeniya A. Mikishanina, “Dynamics of the Chaplygin sphere with additional constraint”, Commun. Nonlinear Sci. Numer. Simul., 117 (2023), 106920–15  mathnet  crossref  isi
    7. Evgeniya A. Mikishanina, “Dynamics of the generalized penny-model on the rotating plane”, Eur. Phys. J. B, 96 (2023), 15–8  mathnet  crossref  isi
    8. Yu. L. Karavaev, “Spherical Robots: An Up-to-Date Overview of Designs and Features”, Rus. J. Nonlin. Dyn., 18:4 (2022), 709–750  mathnet  crossref  mathscinet
    9. G. R. Saypulaev, B. I. Adamov, A. I. Kobrin, “Comparative Analysis of the Dynamics of a Spherical Robot with a Balanced Internal Platform Taking into Account Different Models of Contact Friction”, Rus. J. Nonlin. Dyn., 18:5 (2022), 803–815  mathnet  crossref  mathscinet
    10. E. A. Mikishanina, “Motion Control of a Spherical Robot with a Pendulum Actuator for Pursuing a Target”, Rus. J. Nonlin. Dyn., 18:5 (2022), 899–913  mathnet  crossref  mathscinet
    11. Alexander A. Kilin, Elena N. Pivovarova, “Motion control of the spherical robot rolling on a vibrating plane”, Applied Mathematical Modelling, 109 (2022), 492  crossref
    12. Firdaus E. Udwadia, Nami Mogharabin, “New Directions in Modeling and Computational Methods for Complex Mechanical Dynamical Systems”, Processes, 10:8 (2022), 1560  crossref
    13. Alexander A. Kilin, Elena N. Pivovarova, “A Particular Integrable Case in the Nonautonomous Problem of a Chaplygin Sphere Rolling on a Vibrating Plane”, Regul. Chaotic Dyn., 26:6 (2021), 775–786  mathnet  crossref
    14. Udwadia F.E. Mogharabin N., “The Use of Zero-Mass Particles in Analytical and Multi-Body Dynamics: Sphere Rolling on An Arbitrary Surface”, J. Appl. Mech.-Trans. ASME, 88:12 (2021), 121006  crossref  isi  scopus
    15. Alexey V. Borisov, Evgeniya A. Mikishanina, “Two Nonholonomic Chaotic Systems. Part II. On the Rolling of a Nonholonomic Bundle of Two Bodies”, Regul. Chaotic Dyn., 25:4 (2020), 392–400  mathnet  crossref  mathscinet
    16. 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
    17. E. A. Mityushov, N. E. Misyura, S. A. Berestova, “Kvaternionnaya model programmnogo upravleniya dvizheniem shara Chaplygina”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:3 (2019), 408–421  mathnet  crossref
    18. D. D. Holm, V. Putkaradze, “Dynamics of non-holonomic systems with stochastic transport”, Proc. R. Soc. A., 474:2209 (2018), 20170479  crossref
    19. Alexander A. Kilin, Elena N. Pivovarova, “The Rolling Motion of a Truncated Ball Without Slipping and Spinning on a Plane”, Regul. Chaotic Dyn., 22:3 (2017), 298–317  mathnet  crossref  mathscinet
    20. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics”, Russian Math. Surveys, 72:5 (2017), 783–840  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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