On Lyapunov stability of nonautonomous mechanical systems

A sufficient condition for the linear stability of nonautonomous dissipativ e mechanical systems with circulatory forces is derived. It is applied to a utonomous systems transformed to nonautonomous ones by a time-dependent ort hogonal transformation. This allows to obtain sufficient stability conditio ns in case the perturbed potential energy can have negative values, which w as not possible up to now. This is, in particular, of importance for plasma equilibria with sheared flows. The nearness of the sufficient condition to necessity is discussed for a particular example. (C) 2000 Elsevier Science B.V. All rights reserved.