Applications of the singular value decomposition in dynamics
This article presents some applications of the singular value decomposition of a general rectangular matrix for determining solutions of underdetermined systems which arise in the study of dynamical mechanical systems. First, the theory of the singular value decomposition is exposed briefly. Then, it is shown how periodic solutions of Hamiltonian, conservative systems can be determined in a direct way. Finally, a path following method for the continuation of stationary and periodic solutions and bifurcation points is described. The usefulness of these procedures is shown in examples of a rotor with nonlinear support stiffness and a system which consists of an array of ten nonlinearly coupled oscillators.
scientific article; zbMATH DE number 168852
scientific article