## 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.