Meeting Time: MW, 10:30 - 11:50 Location: NSH 3002
Textbook: The main text for this class is An Introduction to Geometric Mechanics and Differential Geometry. This book is currently under development by the course instructors, and will be updated with new content as the semester progresses. For content that does not appear in the textbook, lectures and notes will be the primary reference, along with relevant papers.Course Description: This course introduces geometric methods for the analysis of locomoting systems. Focusing on the kinematics of locomoting systems, the course covers topics from differential geometry, geometric mechanics, and motion planning . Specific topics include configuration spaces, manifolds, groups, Lie groups, representations of velocity, holonomic and nonholonomic constraints, constraint curvature, response to cyclic inputs and distance metrics. The primary goal of this class is to develop an intuitive understanding of these concepts and how they are used in locomoting systems, rather than working through a set of formal proofs and derivations. We do, however, incorporate enough mathematical formalism for this class to serve as a starting point for further investigation into this topic area. We also call upon biological data, when available, and relate to the mathematical formalisms in the class. Grading: We do not have a strict grading policy, as we expect that all students in the class will do well as long as they put in the work. For a rough scheme of how we might assign grades, we will do approximately half based on homeworks and half based on the project. |