THE MATHEMATICS OF MOTION FOR COMPUTER ANIMATION - A CASE-STUDY

Besides a methodology for the dynamic modeling of a mechanical system, a set of generalized coordinates and one coordinate frame are necessary to describe and render graphically the motion of the system. For animation and control purposes, one coordinate frame might lead to a more efficient or more accurate algorithm than others. Issues to be addressed in the realm of motion animation are rigid-body attitude representation, both holonomic and nonholononmic kinematic constraints and computational complexity. A suitable procedure, based on the natural orthogonal complement, introduced elsewhere, is presented in this paper, which allows a systematic modeling of a mechanical system in any reference frame with any set of generalized coordinates. Various attitude representations and coordinate frames are compared with regard to computational complexity. To illustrate the procedure, a case study, regarding the classical problem of a disk rolling on a plane, is included.