On Classical Newmark Integration of Multibody Dynamics

The use of the classical Newmark method for the integration of Multibody System Dynamics (MBSD) is presented. This approach has the advantage of directly integrating the second order differential equations which appear in MBSD and, thus, does not require duplication of the variables, reducing the computational cost. The resolution of each step is performed in a full Newton approach, instead of using less efficient quasi-Newton approaches. This requires the analytic computation of derivatives, but improves in convergence and precision. An implementation for 2D problems using Newton-Euler formalism and cartesian coordinates has been developed to test the system. An example is included.