On the Stability of Potential Systems under the Action of Non-conservative Positional Forces

The stability of linear mechanical systems with finite numbers of degrees of freedom subjected to potential and non-conservative positional forces is considered. The positive semidefiniteness of the potential energy is assumed. Three new stability criteria which are in a simple way related to the properties of the system matrices are derived. These criteria improve previously obtained results of the same type. Several simple examples are given to illustrate the correctness and applicability of the obtained results.