Impulse-Based Dynamic Simulation of Higher Order and Numerical Results

First, we will provide a short introduction to the impulse-based method for dynamic simulation. Till now, impulses were frequently used to resolve collisions between rigid bodies. In the last years, we have extended these techniques to simulate constraint forces. Important properties of the new impulse method are: (1) Simulation in Cartesian coordinates, (2) complete elimination of the constraint drift known from Lagrange multiplier methods, (3) simple integration of collision and friction and (4) real-time performance even for complex multibody systems like six-legged walking machines. In order to demonstrate the potential of the impulse-based method, we report on numerical experiments. We compare the following dynamic simulation methods: (1) Generalized (or reduced) coordinates, (2) the Lagrange multiplier method with and without several stabilization methods like Baumgarte, the velocity correction and a projection method, (3) impulse-based methods of integration order 2, 4, 6, 8, and 10. We have simulated the mathematical pendulum, the double and the triple pendulum with all of these dynamic simulation methods and report on the attainable accuracy. It turned out that the impulse methods of higher integration order are all of O(h^3) but have very small factors and are therefore relatively accurate. A Lagrange multiplier method fully stabilized by impulse-based techniques turned out to be the best of the Lagrange multiplier methods tested.