Resonant instability in multidimensional Lyapunov systems

The stability of a point of rest of a Lyapunov system, which describes the perturbed motion of a dynamical system with an arbitrary number of degrees of freedom, is investigated. It is assumed that the characteristic equation of the system of the first approximation has a number of imaginary roots, while the quadratic part of the integral is not sign-definite. The case of third-order resonance is considered, when the stability problem is solved by the first non-linear (quadratic) terms. (C) 2012 Elsevier Ltd. All rights reserved.