Mathematical Model of Horse and Rider Interaction during Horse Jumping

To understand the horse-human interaction, their movement during trot are successfully modeled by spring-damper-mass (SDM) models. However, whether the SDM models are applicable to jump is not clear since jump is not an oscillatory. To examine the applicability of the SDM models, we evaluated the prediction ability of the two SDM models, an SDM with a forcing function (Model 1) and an SDM with an active spring-damper system (Model 2), using the trajectories of the centers of gravity of the horse and the rider during jump collected from videos, which include canter and jump. As a result, Both Models 1 and 2 succeeded to predict the observed trajectories for the canter data, however, only Model 2 succeeded during jump for the jump data. This implies that the rider changes its mechanical property during jump.