Jan Bender and Alfred Schmitt, Fast Dynamic Simulation of Multi-Body Systems Using Impulses, Virtual Reality Interactions and Physical Simulations (VRIPhys), 2006


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A dynamic simulation method for multi-body systems is presented in this paper. The special feature of this method is that it satisfies all given constraints by computing impulses. In each simulation step the joint states after the step are predicted. In order to obtain valid states after the simulation step, impulses are computed and applied to the connected bodies. Since a valid joint state is targeted exactly, there is no drift as the simulation proceeds in time and so no additional stabilisation is required. In previous approaches the impulses for a multi-body system were computed iteratively. Since dependencies between joints were not taken into account, the simulation of complex models was slow. A novel method is presented that uses a system of linear equations to describe these dependencies. By solving this typically sparse system the required impulses are determined. This method allows a very fast simulation of complex multi-body systems.

Additional information:

The paper describes another impulse-based simulation method which uses systems of linear equations to determine the required impulses very fast. In my current research I determined a way to solve the system of linear equations in linear time and in linear space.


Car (DivX, Mpeg)

Crash test

Crash test (DivX, Mpeg)

Office toy

Office toy (DivX, Mpeg)


Tree with 127 bodies and joints (DivX, Mpeg)


Walker (DivX, Mpeg)