A time integration algorithm for flexible mechanism dynamics: The DAE α-method Original Research Article

This paper introduces a new family of second-order methods for solving the index-2 differential-algebraic equations (DAEs) of motion for flexible mechanism dynamics. These methods, which extend the α-methods for ODEs of structural dynamics to DAEs, possess numerical dissipation that can be controlled by the user. Convergence and stability analysis is given and verifies that the DAE α-methods introduce no additional oscillations and preserve the stability of the underlying ODE system. Convergence of the Newton iteration, which can be a source of difficulty in solving nonlinear oscillatory systems with large stepsizes, is achieved via a coordinate-split modification to the Newton iteration. Numerical results illustrate the effectiveness of the new methods for simulation of flexible mechanisms.