Singular Value Decomposition for Constrained Dynamical Systems

Abstract

The method of singular value decomposition is shown to have useful application to the problem of reducing the equations of motion for a class of constrained dynamical systems to their minimum dimension. This method is shown to be superior to classical Gaussian elimination for several reasons: (i) The resulting equations of motion are assured to be of full rank. (ii) The process is more amenable to automation, as may be appropriate in the development of a computer program for application to a generic class of systems. (iii) The analyst is spared the responsibility for the selection of specific coordinates to be eliminated by substitution in each individual case, a selection that has no physical justification but presents abundant risk of mathematical contradiction. This approach is shown to be very efficient when the governing dynamical equations are derived via Kane’s method.