Explicit Higher-Order Integrator for Multibody Dynamics

Apart from other options, a common procedure to integrate order 2 Ordinary Differential Equations (ODEs) present in Multibody systems is to reduce the order of the ODE by duplicating the number of variables. This leads to apply the well-known family of Runge-Kutta (RK) methods. Other approach, commonly used in structural mechanics, is the use of methods developing to integrate directly the ODE without increasing the number of variables. These are usually named after “Structural integrators”. An important drawback when using RK methods is that, when one tries to apply them to Differential Algebraic Equations (DAEs); they require a reduction of the DAE index, which lead to the need of stabilization methods to remove the drift. In this paper, a new integrator for the direct integration of order 2 ODEs is presented. This method is similar in concept to the commonly used Central Difference method for structural dynamics and allows one to develop algorithms with different properties related to convergence order and stability. The method presented uses 5th order of derivatives (5th degree) to reach a 6 order convergence and is configurable using parameters. Some sets of parameters, which are of interest, have been studied and some examples belonging to multibody dynamics are presented.