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This article is cited in 8 scientific papers (total in 8 papers)
Nonholonomic mechanics
Stability of Steady Rotations in the Nonholonomic Routh Problem
A. V. Borisov, A. A. Kilin, I. S. Mamaev Institute of Computer Science, Udmurt State University,
ul. Universitetskaya 1, Izhevsk, 426034 Russia
Abstract:
We have discovered a new first integral in the problem of motion of a dynamically symmetric ball, subject to gravity, on the surface of a paraboloid. Using this integral, we have obtained conditions for stability (in the Lyapunov sense) of steady rotations of the ball at the upmost, downmost and saddle point.
Keywords:
nonholonomic constraint, stationary rotations, stability.
Received: 04.10.2007 Accepted: 16.01.2008
Citation:
A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Stability of Steady Rotations in the Nonholonomic Routh Problem”, Regul. Chaotic Dyn., 13:4 (2008), 239–249
Linking options:
https://www.mathnet.ru/eng/rcd574 https://www.mathnet.ru/eng/rcd/v13/i4/p239
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