Abstract
The problem of the stability of stationary motions (SM) of mechanical systems admitting of first integrals and a function that does not grow along the motions is considered. Theorems are proposed on the stability and asymptotic stability in parts of the variables, as well as on the instability of the SM of such systems. The general situations are illustrated with an example of the motion of a heavy inhomogeneous sphere over a plane with friction.
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