A contribution to the stability of nonholonomic systems

There are nonholonomic systems whose stability at equilibrium points with respect to some variables can be determined from the stability with respect to only part of these variables. In particular, for the nonholonomic systems with the limitation that the coefficients of nonholonomic constraints are bounded on the domain Δ, an equilibrium position is stable with respect to all the variables if it is stable with respect to some of the variables. A good example is the well known Chaplygin system. Propositions and corollaries are given, that are useful for simplifying the study of the stability of these nonholonomic systems at the equilibrium points.