A Fast Explicit Integrator for Numerical Simulation of Multibody System Dynamics

A computationally efficient explicit integrator is proposed to solve the differential-algebraic equations (DAEs) in multibody system dynamics. Algebraic constraint equations in the DAEs are regularized by a simple stabilization method, yielding a set of first order ordinary differential equations (ODEs), whose large eigenvalues are located at the negative real axis. Those ODEs have specific stiff characters, and are integrated by a class of explicit integrators (the Runge-Kutta-Chebyshev family of ODE integrators) with large stability zones on the negative real axis, so as to achieve large step-sizes at the same requirement of accuracy. The integrator adopted in this work is of fourth order, verified by practical example, and compared to several popular integrators. The high efficiency of the explicit integrator renders it a good option for practical simulations of the dynamics of constraint mechanical systems.