Department of Computational and Applied Mathematics 6100 Main, MS-134 Rice University Houston, TX 77251-1892
We suggest an investigation for the simulation and control of dynamical systems governed by Lagrangian equations of motion. Ordinarily, these equations employ three-space representations of rotational motion. However, we propose to employ four-space Euler parameters to describe the rotational components of motion within the governing differential equations. Euler parameters have the advantage of being nonsingular and well-behaved for arbitrary rotations. In our apporach to developing direct Euler parameter-based numerical algorithms for modeling the time-evolving interaction of both rigid and deformable bodies within a dynamical system, we will illustrate special cases and simplified situations with the aim of revealing more generally applicable concepts and points of view. In turn, these concepts can serve as guides to solving more difficult problems in relation to constrained motion.
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