A simple approximation to rigid body dynamics for computer animation

Recently, the dynamics of linked articulated rigid bodies has become a valuable tool for making realistic three-dimensional computer animations. An exact treatment of rigid body dynamics, however, is based on rather non-intuitive results from classical mechanics (e.g. the Euler equations for rotating bodies) and it relies heavily on sophisticated numerical schemes to solve (large) sets of coupled non-linear algebraic and differential equations. As a result, articulated rigid bodies are not yet supported by most real-time animation systems. This paper discusses an approach to rigid body dynamics which is based on (both conceptually and algorithmically much simpler) point mechanics; this gives rise to an asymptotically exact numerical scheme (NSI) which is useful in the context of real-time animation, provided that the number of degrees of freedom of the simulated system is not too large. Based on NSI, a second scheme (NS2) is derived which is useful for approximating the motions of linked articulated rigid bodies; NS2 turns out to be sufficiently fast to give at least qualitative results in real-time simulation. In general, the algorithm NS2 is not necessarily (asymptotically) exact, but a quantitative analysis shows that in the absence of reaction forces it conserves angular momentum.