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Regul. Chaotic Dyn., 2013, Volume 18, Issue 1-2, Pages 159–165 (Mi rcd102)  

This article is cited in 11 scientific papers (total in 11 papers)

On the Motion of a Mechanical System Inside a Rolling Ball

S. V. Bolotinab, T. V. Popovac

a University of Wisconsin–Madison, 480 Lincoln Dr., Madison, WI 53706-1325, USA
b V. A. Steklov Mathematical Institute of Russian Academy of Sciences, Gubkina 8, Moscow, 119991 Russia
c M. V. Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991 Russia

Abstract: We consider a mechanical system inside a rolling ball and show that if the constraints have spherical symmetry, the equations of motion have Lagrangian form. Without symmetry, this is not true.

Keywords: nonholonomic constraint, rolling ball, Lagrange equations, Hamilton principle

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 11.G34.31.0039
This research was done at the Udmurt State University and was supported by the Grant Program of the Government of the Russian Federation for state support of scientific research conducted under the supervision of leading scientists at Russian institutions of higher professional education (Contract ¹11.G34.31.0039). Also supported by the Programme “Dynamical Systems and Control Theory”.


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MSC: 37J60, 70H03, 70E18
Received: 12.12.2012

Citation: S. V. Bolotin, T. V. Popova, “On the Motion of a Mechanical System Inside a Rolling Ball”, Regul. Chaotic Dyn., 18:1-2 (2013), 159–165

Citation in format AMSBIB
\by S. V. Bolotin, T. V. Popova
\paper On the Motion of a Mechanical System Inside a Rolling Ball
\jour Regul. Chaotic Dyn.
\yr 2013
\vol 18
\issue 1-2
\pages 159--165

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    This publication is cited in the following articles:
    1. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Dinamika negolonomnykh sistem, sostoyaschikh iz sfericheskoi obolochki s podvizhnym tverdym telom vnutri”, Nelineinaya dinam., 9:3 (2013), 547–566  mathnet
    2. A. V. Borisov, I. S. Mamaev, A. V. Tsiganov, “Non-holonomic dynamics and Poisson geometry”, Russian Math. Surveys, 69:3 (2014), 481–538  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Dynamics of Nonholonomic Systems Consisting of a Spherical Shell with a Moving Rigid Body Inside”, Regul. Chaotic Dyn., 19:2 (2014), 198–213  mathnet  crossref  mathscinet  zmath
    4. Yu. L. Karavaev, A. A. Kilin, “Dinamika sferorobota s vnutrennei omnikolesnoi platformoi”, Nelineinaya dinam., 11:1 (2015), 187–204  mathnet  elib
    5. Alexander P. Ivanov, “On the Control of a Robot Ball Using Two Omniwheels”, Regul. Chaotic Dyn., 20:4 (2015), 441–448  mathnet  crossref  mathscinet  zmath  adsnasa  elib
    6. Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “Dynamics and Control of an Omniwheel Vehicle”, Regul. Chaotic Dyn., 20:2 (2015), 153–172  mathnet  crossref  mathscinet  zmath  adsnasa
    7. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Hamiltonization of elementary nonholonomic systems”, Russ. J. Math. Phys., 22:4 (2015), 444–453  crossref  mathscinet  zmath  isi  scopus
    8. Yury L. Karavaev, Alexander A. Kilin, “The Dynamics and Control of a Spherical Robot with an Internal Omniwheel Platform”, Regul. Chaotic Dyn., 20:2 (2015), 134–152  mathnet  crossref  mathscinet  zmath  adsnasa  elib
    9. Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “Dynamics of the Chaplygin Sleigh on a Cylinder”, Regul. Chaotic Dyn., 21:1 (2016), 136–146  mathnet  crossref  mathscinet  zmath  elib
    10. V. Putkaradze, S. Rogers, “On the dynamics of a rolling ball actuated by internal point masses”, Meccanica, 53:15 (2018), 3839–3868  crossref  mathscinet  isi  scopus
    11. Putkaradze V. Rogers S., “on the Optimal Control of a Rolling Ball Robot Actuated By Internal Point Masses”, J. Dyn. Syst. Meas. Control-Trans. ASME, 142:5 (2020)  crossref  isi  scopus
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