On the stability of motion

Abstract

A theorem on uniform asymptotic stability of the origin for a differential system is proved, using two auxiliary functions: a Liapunov function and a "Liapunovlike" vector function. A theorem on instability is also proved. The results are applied to a system of Lagrange equations with complete dissipation and non energic forces: in this case, the Liapunov function is the total energy and the Liapunovlike vector function is the vector of the conjugate momenta. © 1968.