Animal Shapes, Modal Analysis, and Visualization of Motion (I): Horse and Camel

Eigenfunctions and eigenvalues of physical systems and engineering structures can reveal many of the system’s fundamental features and, therefore, become a basis for the study of inverse problems. In this series of papers, we take a reverse, direct-problem point of view; namely, given the shapes of animals, can we see the patterns of their motions or behaviors through their eigenmode analysis? This modal analysis, we believe, has never been done for living animals. Our modal analysis emphasizes dynamics, which is achieved by visualization through video animation by incorporating the time-harmonic dependence of the eigenmodes. Furthermore, we intend our modal analysis to be more realistic by encompassing the situation of the presence of a floor. Certain physical interpretations of the motion patterns from modal analysis are made. In addition, by visualization, one can see that symmetry plays an important role in motion patterns. One of our main conclusions is that shapes alone can usefully reflect or explain some animal’s behavior or motion patterns.