Criteria for Pervasive Damping of Mechanical Systems with First Integrals of Motion

Abstract

AbstractThis paper determines necessary and sufficient criteria for pervasive (or complete) damping of mechanical systems with first integrals of motion. The pervasiveness of the damping is essential when the stability of a system is investigated through its linearized set of equations of motion by Liapunov's method: the sufficient conditions for asymptotic stability then become necessary conditions. The existence of first integrals of motion restricts the asymptotic stability to a certain class of initial conditions. The pervasiveness of the damping will be considered in the same sense.