Orthogonal square root eigenfactor parameterization of mass matrices
Additional Document Info
1997, American Institute of Aeronautics and Astronautics, Inc. An improved method is presented to parameterize a smoothly time varying symmetric, positive definite system mass matrix M(t) in terms of the instantaneous eigenfactors, namely the eigenvalues and eigenvectors of M(t). Differential equations are desired whose solutions generate the instantaneous spectral decomposition of M(t). The derivation makes use of the fact that the eigenvector matrix is orthogonal and thus evolves analogously to a higher dimensional rotation matrix. Careful attention is given to cases where some eigenvalues and/or their derivatives are equal or near-equal. A robust method is presented to approximate the corresponding eigenvector derivatives in these cases, which ensures that the resulting eigenvectors still diagonalize the instantaneous M(t) matrix. This method is also capable of handling the rare case of discontinuous eigenvectors which may only occur if the corresponding eigenvalues and their derivatives are equal.