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
Citation:
Borisov A. V., Kilin A. A., Mamaev I. S., Stability of Steady Rotations in the Nonholonomic Routh Problem, Regular and Chaotic Dynamics,
2008, Volume 13, Number 4,
pp. 239-249