Computer simulation of the dynamics of rigid bodies interacting through collisions, stacks and joints is performed using a constraint-based system in which constraints are defined in terms of the positions of the bodies. Displacements caused by reaction forces necessary to ensure that the bodies comply with the position constraints can be calculated and can be done iteratively by updating equations defining the reaction forces and the displacements such that the computation time and memory resources required to perform the calculations is linearly dependent upon the number of bodies and the number of contacts and joints between the bodies. Computational requirements and memory requirements are reduced further by performing the calculations using vector operations.