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.
Keywords:
nonholonomic constraint, stationary rotations, stability
Citation:
Borisov A. V., Kilin A. A., Mamaev I. S., Stability of steady rotations in the non-holonomic Routh problem, Rus. J. Nonlin. Dyn.,
2006, Vol. 2, No. 3,
pp. 333-345
DOI:10.20537/nd0603006