Geometric Mechanics and Optimal Coordinates for Locomotion

Event Details

Date/Time:

  • Wednesday, March 6, 2013 3:00 pm - 4:00 pm
Location: Klaus 1116 East
Phone: (404) 894-8886
Fee(s): Free

For More Information Contact

alison.morain@physics.gatech.edu

School of Physics Nonlinear Science & Mathematical Physics: Presenting Ross Hatton, Oregon State University

Understanding the locomotion of animals and robots can be a challenging problem, involving nonlinear dynamics and the coordination of many degrees of freedom. Geometric mechanics offers a vocabulary for discussing these dynamics in terms of lengths, areas, and curvatures. In particular, a tool called the *Lie bracket* combines these geometric concepts to describe the effects of cyclic changes in the locomotor's shape, such as the gaits used by walking or crawling systems.

In this talk, I will introduce some basic principles of geometric mechanics, and show how they provide insight into the locomotion of undulating systems (such as snakes and micro-organisms). I will then discuss my work on how coordinate representations affect the information provided by the geometric structures, and show that the choice of coordinates for a given system can be optimized in a simple, fundamental manner. Finally, I will demonstrate that the geometric techniques are useful beyond the "clean" ideal systems on which they have traditionally been developed, and can provide insight into the motion of systems with considerably more complex dynamics, such as locomotors in granular media.

Map of Georgia Tech

Georgia Institute of Technology
North Avenue, Atlanta, GA 30332
Phone: 404-894-2000