The simplest model possible for bouncing systems consists of a point mass bouncing passively on a mass-less spring without viscous losses. This type of spring-mass model has been used to describe the stance period of symmetric running gaits. In this study, we investigated the interaction between horse and rider at trot using three models of force-driven spring (-damper)-mass systems. The first system consisted of a spring and a mass representing the horse that interact with another spring and mass representing the rider. In the second spring-damper-mass model, dampers, a free-fall and a forcing function for the rider were incorporated. In the third spring-damper-mass model, an active spring system for the leg of the rider was introduced with a variable spring stiffness and resting length in addition to a saddle spring with fixed material properties. The output of the models was compared with experimental data of sitting and rising trot and with the modern riding technique used by jockeys in racing. The models show which combinations of rider mass, spring stiffness and damping coefficient will result in a particular riding technique or other behaviours. Minimization of the peak force of the rider and the work of the horse resulted in an `extreme` modern jockey technique. The incorporation of an active spring system for the leg of the rider was needed to simulate rising trot. Thus, the models provide insight into the biomechanical requirements a rider has to comply with to respond effectively to the movements of a horse.
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