On the stability of linear nonconservative systems

Abstract

For a system of linear second-order differential equations, a stability criterion is derived which gives a simple relation between eigenvalues of two of the coefficient matrices and an estimate of the lower bound | λ | min {\left | \lambda \right |_{\min }} of the eigenvalue for the nonlinear eigenvalue problem of the total system. Estimations of | λ | min {\left | \lambda \right |_{\min }} are given, and applications of the stability criterion are shown by numerical examples.