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This article is cited in 32 scientific papers (total in 32 papers)
Rolling of a Non-homogeneous Ball Over a Sphere Without Slipping and Twisting
A. V. Borisov, I. S. Mamaev Institute of Computer Science, Udmurt State University,
Universitetskaya ul. 1, Izhevsk 426034, Russia
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, J. Koiller and K. 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:
nonholonomic mechanics, reducing multiplier, hamiltonization, isomorphism.
Received: 09.12.2006 Accepted: 28.02.2007
Citation:
A. V. Borisov, I. S. Mamaev, “Rolling of a Non-homogeneous Ball Over a Sphere Without Slipping and Twisting”, Regul. Chaotic Dyn., 12:2 (2007), 153–159
Linking options:
https://www.mathnet.ru/eng/rcd618 https://www.mathnet.ru/eng/rcd/v12/i2/p153
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