Geometric Mechanics: A Framework for Studying Animal Locomotion
Abstract
We demonstrate the utility of geometric mechanics in studying various types of animal locomotion. Geometric mechanics offers a useful set of tools, including connection vector fields and height functions, for analyzing biological movements in an intuitive manner. These tools were conventionally applied to systems with only two internal degrees of freedom, but they can be modified to model locomotors that have many joints. We present case studies of two types of locomotions: crutching motion of mudskippers and sidewinding in sidewinder rattlesnakes (Crotalus cerastes). In the mudskipper study, geometric analysis shows tail usage can either be harmful, neutral, or beneficial depending on limb-tail coordination. This result shows control of limb-tail movement is crucial in achieving effective movements. C. cerastes moves by generating posteriorly traveling body waves in the horizontal and vertical directions with ±90 degrees phase offset. Geometric analysis shows speed of sidewinding sensitively depends on wave kinematics. Subtle changes in kinematics can significantly change locomotion performance. Geometric analysis show the fastest sidewinding movement is achieved when the phase offset is equal to ±90 degrees, revealing sidewinders use the set of wave kinematics which produces high locomotion speed. Together, these examples highlight the diversity of systems for which geometric mechanics can provide useful mathematical insights.
BibTeX
@conference{Gong-2016-122401,author = {C. Gong and H. Astley and J. Dai and B. Mclnroe and P. E. Schiebel and M. Travers and D. Goldman and H. Choset},
title = {Geometric Mechanics: A Framework for Studying Animal Locomotion},
booktitle = {Proceedings of Society for Integrative and Comparative Biology Annual Meeting (SICB '16)},
year = {2016},
month = {January},
volume = {56},
pages = {77},
}