Instability Degree and Singular Subspaces of Integral Isotropic Cones of Linear Systems of Differential Equations

Abstract

The instability degree of linear systems of differential equations is estimated in terms of the dimensions of completely singular subspaces of integral cones of these systems. Special attention is given to the case where the linear system under study has first integrals of the type of nonsingular quadratic forms. General results are applied to a well-known problem concerning the gyroscopic stabilization of unstable equilibria of a mechanical system.