Proceedings PaperCombining three-dimensional solid modeling with the geometry of the behavior of a dynamical system
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Combining the geometry of the behavior of dynamical systems with a computer generated solid model creates a complete environment for mechanical and visual feedback. Dynamical systems are represented mathematically by non-linear coupled differential equations. The investigation of the equations usually is limited to the behavior of the parameter space. When inconsistencies arise between the mathematical model and the physical system, either the model is modified or laboratory tests are conducted on the physical system. It is possible to combine these two methodologies. Using a commercial modeller, a physical model can be constructed for the system under investigation, in this example a single-legged, hopping robot. The state equations for hopping robots in laboratory environments are well documented and extensively researched. By programming the modeller's animation keyframes with the appropriate script of time- and space-dependent motion amplitudes derived from the mathematical model, all of the individual functioning components can be subjected to their appropriate dynamics. A manifold visualizer was developed that computes a manifold of the geometry's behavior that can be viewed at the same time as the physical model is animated. The complete virtual environment has both the system dynamics and the physical modelling feedback.