ABSTRACT
The use of dynamics is becoming a standard technique in computer animation. This technique has the advantages of producing realistic motion and requiring a modest amount of control input. There have been two main problems associated with the use of dynamics in computer animation. The first problem is controlling the motion produced by the dynamics simulations. Simple motions, from a physical point of view, are easy to produce, but complicated motions can be quite difficult. The dynamics simulations are driven by forces and torques, which are not a natural way of specifying motion for most animators. In order to profitably use dynamics, control techniques that can automatically produce these forces and torques are required. The other main problem is the development of numerical techniques for solving the equations of motion. We would like these techniques to be efficient, so interactive control of the motion is possible, and at the same time they must be very stable. The differential equations used in articulated figure animation tend to be quite stiff, and this leads to stability problems in their solution. At first these two problems appear to be unrelated, but there is a strong relationship between them. The control techniques are the main contributors to the stiffness of the equations and the problems involved in their numerical solution. Similarly, the available solution techniques dictate the control techniques that can be used. For example, if the solution techniques are too slow, interactive
control is not possible. In this chapter, we investigate control techniques and solution techniques for the equations of motion. We also investigate the relationships between them.
