Collaborative Research: Ergodic Trajectories in Discrete Mechanics

How should a mechanical system search an environment, ensuring coverage while respecting physical constraints dictated by the physics? Ergodic trajectories are trajectories that have time histories that match a spatial distribution function. Some mechanical systems are naturally ergodic with respect to a distribution function that provides coverage—chaotic systems often have this characteristic. If a mechanical system doesn’t naturally satisfy ergodicity, it can be sometimes be designed to be ergodic by parametric changes, topological changes, and changes in forcing. However, this design process requires numerical methods that both respect the mechanics of the physical system and the statistics of distribution functions. Structured integration techniques have shown great promise in both these respects, and the proposed work will address numerical methods in the ergodic design of mechanical systems. Keywords: Discrete Mechanics, Interconnected Dynamic Systems, Statistical Methods