Application of Bloch Analysis to the Stability Investigation of Hamiltonian Systems of Linear Differential Equations with Periodic Coefficients

Abstract

AbstractThe direct integral decomposition of the self‐adjoint operator associated with the differential equation is used to determine the set of parameters for which the equilibrium solution is stable. For systems with more than one degree of freedom even parameters in the interior of the spectrum may give rise to instability. The possibility of approximation of the eigenvalues without numerical solution of the differential equation, the qualitative behaviour considering small perturbations and the relation to Krein's stability theory are outlined. The described method is applied to models of two‐bladed wind turbines.