On the Use of HalfImplicit Numerical Integration in Multibody Dynamics

Abstract

This work highlights the use of halfimplicit numerical integration in the context of the index three differential algebraic equations (DAEs) of multibody dynamics. Although halfimplicit numerical integration is well established for ordinary differential equations problems, to the best of our knowledge, no formal discussion covers its use in the context of index three DAEs of multibody dynamics. We wish to address this since when compared to fully implicit methods, halfimplicit integration has two attractive features: (i) the solution method does not require the computation of the Jacobian associated with the constraint, friction, contact, or userdefined applied forces; and (ii) the solution is simpler to implement. Moreover, for nonstiff problems, halfimplicit numerical integration yields a faster solution. Herein, we outline the numerical method and demonstrate it in conjunction with three mechanisms. We report on convergence order behavior and solution speed. The Python software developed to generate the results reported is available as open in a public repository for reproducibility studies.