Year of Graduation
2024
Level of Access
Open Access Thesis
Embargo Period
5-16-2024
Department or Program
Physics and Astronomy
First Advisor
Dale Syphers
Second Advisor
Amy Johnson
Abstract
The Froude number is the ratio of kinetic energy to gravitational potential energy used during locomotion and is often used to analyze gait transitions. Here, I compare and contrast the human walk-run gait transition, which occurs at a consistent Froude number of 1 because there exists a mechanical speed limit to walking, and the sea star crawl-bounce gait transition, which occurs around Froude numbers of 1*10^-3. In this thesis I investigate why sea stars exhibit two gaits despite lacking brains and moving at Froude numbers far below other known gait transitions, hypothesizing (1) that the crawl-bounce transition may be mechanical and thus still depends on the Froude number, and (2) that the crawl-bounce transition is best modeled gradually compared to the instantaneous human walk-run transition. Thirty sea stars were filmed and the resulting kinematic data is used here to inform thinking about the crawl-bounce transition. I first discuss damped driven harmonic motion of a single oscillator, but eventually turn to using coupled oscillators and deriving that a coupling constant between metronomes on a moving base is the Froude number, which is therefore relevant for the crawl-bounce transition. I lastly discuss a purely mathematical analogue of the crawl-bounce transition as a Hopf bifurcation in horizontal speed and vertical velocity phase space, which leads to a rough model with results qualitatively similar to observed kinematic data from films, and indicates that a gradual transition is in fact a good fit for the crawl-bounce transition.