Asymptotic motions of nonholonomic Chaplygin systems (Q758237)

The existence of asymptotic motions in the neighborhood of an equilibrium configuration that is a center of attraction for them, is of great interest because for a good class of holonomic conservative systems these motions are accompanied by instability of the equilibrium configuration as well as its roughness, i.e., its indestructibility with a sufficiently small ``stirring'' of the corresponding equations. It turns out that an analogous situation holds for nonholonomic Chaplygin systems as well. In this paper we are able to prove, for a certain class of such systems, developing the approach proposed by the author in Ukr. Mat. Zh. 37, No.1, 124-127 (1985), the existence of phase trajectories bordering on an equilibrium configuration as \(t\to \infty\) and \(t\to -\infty\), and the rough instability of the latter.