Animal Shapes, Modal Analysis, and Visualization of Motion (II): Dynamics and Fourier Decomposition

This paper begins with solving the linear elastodynamic equation with forcing by expanding it into Fourier series. We then proceed to prove the conservation laws of momentum, angular momentum, and energy. We intend the paper to provide a computational demonstration for modal analysis by showing that eigenmodes and frequencies of vibration of a free-suspending horse match with the modal analysis results of the horse after a short-impulse impact of the horse with a wall. The horse CAD model has to be modified to contain a rigid body portion to prevent the rotational-tumbling modes. A fast Fourier transform is applied to the sensorial time series data in the calculation of the vibration frequencies. One can see that many low-frequency modes and data match these modal analysis results.