Third-Order Differential-Algebraic Equations for Improved Integration of Multibody Dynamics

This paper introduces the concept of third-order differential-algebraic equations (DAE) for dynamics of constrained multibody systems. Third-order DAE provide jerk of components which can be integrated simultaneously with acceleration to provide improved simulation accuracy. A new Obreshkov predictor-corrector multistep integrator was developed to test this concept. Results from simulations of two planar mechanisms indicate that third-order DAE can reduce computation time by a factor of ten with equivalent accuracy compared to classical methods.