ME Seminar May 9
|Event Date:||May 9, 2013|
|Hosted By:||Mechanical Engineering
|Location:||ME 2054, WL campus
When animals walk their motion appears time-periodic in the body frame. However, in the spatial frame they translate and rotate by a fixed amount with each stride. Thus walking appears to be, not periodic, but relatively periodic with respect to an SE(2)-symmetry. A similar characterization exists for swimming and the pumping of viscous fluids with respect to particle relabeling symmetries and isometries. In summary, relatively periodic phenomena are ubiquitous. The frequency by which we observe these phenomena suggests that they may be robust and dynamically stable as well. In other words, perhaps these phenomena are manifestations of relative limit cycles. In this talk we will find sufficient conditions to assert the existence of relative limit cycles in dissipative Lagrangian systems with an aim towards unifying this range of phenomena.
Henry Jacobs is currently a post-doctoral research associate in Mathematics at Imperial College London. He received his B.A. degree in Applied Mathematics at New York University in 2008 and his Ph.d degree in Control and Dynamical Systems at the California Institute of Technology in 2012. His current research applies geometric descriptions of fluid-structure interaction and complex fluids to various problems, ranging from bio-locomotion to image matching. His recent work with Dr. Joris Vankerschaver revealed that the configuration space for fluid-structure interaction is a special case of a well-studied object in symplectic geometry, called a Lie groupoid. This led to the discovery that small, time-periodic forces on the shape of a body immersed in a fluid can (to arbitrarily good approximation) lead to stable and regular motion, e.g. swimming. Similar geometric methods are currently being used to study terrestrial locomotion (e.g. bipedal walking) with Dr. Jaap Eldering, as well as pumping of complex fluids. Further applications exist within the field of medical imaging, wherein one seeks to use the diffeomorphism group to match images. The result is a new class of particle methods for applications such as medical imaging, liquid crystals, and plasma models; a computationally tractable model for one such particle method (particles in Euclidean space) is presently under construction.