Passive Elasticity in a Model of Snake Locomotion

Snake locomotory dynamics is an interesting field of study to biologists, physicists, and undergraduate applied mathematicians. In this project, we study a simple model problem of an elastic beam moving on a frictional surface. The beam could model an elastic tail of a snake or a sand-swimming lizard. Previous studies have laid out a great deal of groundwork on the motions of bodies with prescribed shapes, but less work has been done on the motions of elastic bodies. To that end, this project incorporates passive elasticity into the model using a fourth-order partial differential equation system that draws from Euler-Bernoulli beam dynamics with the ultimate goal of exploring how various external and internal forces affect both short-term movements and long-term dynamics of the snake body. This work can be extended to studies in robotics, physics, and fluids.