Generalizing Deformable System Dynamics beyond Euclidean Geometry

The study of motion is one of the fundamental concepts in classical physics. While it has been a subject of study for centuries, it was developed for euclidean geometry, which is our everyday experience. We investigate how the mechanics of extended body systems is affected by the presence of curvature. Although we are initially interested in the dynamics of systems in curved space, we plan to apply our framework to other systems with internal degrees of freedom. This framework can span self-propulsion of microorganisms to deformable soft robotic systems both of which can locomote and interact with their environment. Our goal is to develop a physics engine for deformable bodies in curved space which can handle internal degrees of freedom, rigidity constraints, and collisions between objects. The physics engine is used to probe and visualize how the presence of curvature affects the dynamics of deformable systems. Through the simulation of these nonintuitive deformable systems, we hope to gain deeper insight in dynamical deformable systems in flat space and systems with controls.