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Nelin. Dinam., 2006, Volume 2, Number 4, Pages 445–452 (Mi nd183)  

This article is cited in 8 scientific papers (total in 8 papers)

Rolling of a heterotgeneous ball over a sphere without sliding and spinning

A. V. Borisovab, I. S. Mamaevab

a Udmurt State University
b Institute of Computer Science

Abstract: Consider the problem of rolling a dynamically asymmetric balanced ball (the Chaplygin ball) over a sphere. Suppose that the contact point has zero velocity and the projection of the angular velocity to the normal vector of the sphere equals zero. This model of rolling differs from the classical one. It can be realized, in some approximation, if the ball is rubber coated and the sphere is absolutely rough. Recently, Koiller and Ehlers pointed out the measure and the Hamiltonian structure for this problem. Using this structure we construct an isomorphism between this problem and the problem of the motion of a point on a sphere in some potential field. The integrable cases are found.

Keywords: Chaplygin ball, rolling model, Hamiltonian structure.

Full text: PDF file (162 kB)

Document Type: Article
UDC: 532.5
MSC: 37N15

Citation: A. V. Borisov, I. S. Mamaev, “Rolling of a heterotgeneous ball over a sphere without sliding and spinning”, Nelin. Dinam., 2:4 (2006), 445–452

Citation in format AMSBIB
\by A.~V.~Borisov, I.~S.~Mamaev
\paper Rolling of a heterotgeneous ball over a sphere without sliding and spinning
\jour Nelin. Dinam.
\yr 2006
\vol 2
\issue 4
\pages 445--452

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    This publication is cited in the following articles:
    1. A. Yu. Moskvin, “Rezinovyi shar na ploskosti: kriticheskie resheniya”, Nelineinaya dinam., 6:2 (2010), 345–358  mathnet
    2. A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Kak upravlyat sharom Chaplygina pri pomoschi rotorov”, Nelineinaya dinam., 8:2 (2012), 289–307  mathnet
    3. A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “Kachenie bez vercheniya shara po ploskosti: otsutstvie invariantnoi mery v sisteme s polnym naborom integralov”, Nelineinaya dinam., 8:3 (2012), 605–616  mathnet
    4. Alexey V. Borisov, Ivan S. Mamaev, Dmitrii V. Treschev, “Rolling of a rigid body without slipping and spinning: kinematics and dynamics”, J. Appl. Nonlinear Dyn., 2:2 (2013), 161–173  mathnet  crossref
    5. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Ierarkhiya dinamiki pri kachenii tverdogo tela bez proskalzyvaniya i vercheniya po ploskosti i sfere”, Nelineinaya dinam., 9:2 (2013), 141–202  mathnet
    6. A. A. Kilin, Yu. L. Karavaev, A. V. Klekovkin, “Kinematicheskaya model upravleniya vysokomanevrennym mobilnym sferorobotom s vnutrennei omnikolesnoi platformoi”, Nelineinaya dinam., 10:1 (2014), 113–126  mathnet
    7. A. A. Kilin, Yu. L. Karavaev, “Kinematicheskaya model upravleniya sferorobotom s neuravnoveshennoi omnikolesnoi platformoi”, Nelineinaya dinam., 10:4 (2014), 497–511  mathnet
    8. Kovalev O.B., Kovaleva I.O., “Modeling of the Random Packing of a Loose Layer of Polydisperse Spherical Particles”, J. Appl. Mech. Tech. Phys., 55:4 (2014), 709–717  crossref  mathscinet  isi  elib  elib  scopus
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