Eigensolution continuation by projection sensitivity of minimal coordinate set multibody systems

Constrained dynamics problems naturally result in systems of differential-algebraic equations, which can be reduced to the underlying systems of ordinary differential equations with the minimum required number of coordinates using projection algorithms. Their linearization about a steady reference solution can be interpreted as a generalized eigenproblem whose eigensolution represents the spectrum of the problem in that configuration. The eigensolution sensitivity to the original problem's specific parameters of interest may provide useful insight into the system's dynamic characteristics. Building on an original continuation approach for updating the coordinate projection matrix, the sensitivity of the eigensolution is here formulated and analyzed in analytical and numerical form for simple, yet illustrative, problems.