Abstract of Talk by Donald C. Williams

Computational Applications of Lagrangian Equations of Motion to Spatial Loose-Parts Dynamical Systems

Department of Computational and Applied Mathematics
6100 Main, MS-134
Rice University  
Houston, TX 77251-1892

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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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