Stability of steady rotations in the non-holonomic Routh problem
2006, Vol. 2, No. 3, pp. 333-345
Author(s): Borisov A. V., Kilin A. A., Mamaev I. S.
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 in the upmost, downmost and saddle point.
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