ON THE NUMERICAL-INTEGRATION OF THE ROLLING BALL EQUATIONS USING GEOMETRICALLY EXACT ALGORITHMS

In this paper, new types of numerical integration algorithms developed by the authors are described. The main aim of the algorithms is to nu merically integrate differential equations that evolve on geometric ob jects, such as the rotation group and Euclidean group. The algorithms provide iterates that lie on the prescribed geometric object, either e xactly or to some prescribed accuracy, independent of the order of the algorithm. In this sense the algorithms can be called geometrically e xact integration algorithms. The paper also describes the application of these new algorithms to the nonholonomic dynamic equations that des cribe a ball rolling on a flat table, using the kinematic evolution in the Euclidean group.