A modal analysis comparison of Lagrangian descriptor models

The generalized eigenvalue problem for descriptor models are compared based on Lagrangian differential-algebraic equations (DAE) of motion for discrete systems. The DAE are linearized using a local, indirect approach and alternate descriptor representations are obtained. The eigenvalues and eigenvectors for these alternate representations are compared using a simple numerical example. Results include the identification of spurious zero eigenvalues, interpretation of constraint-related infinite eigenvalues, and interpretation of the additional information contained in the eigenvectors of systems with "excess" descriptors.