Mathematical model of a horse rider simulator and its program implementation in the “Wolfram Mathematica” computer mathematics system

Riding simulation machines allow training horse-back riders regardless of environmental and weather conditions, horse fatigue, stable remoteness and other factors. Riders can practice complex movements without fear of potential injury related to sometimes unpredictable behavior of the horse. This type of training machines requires special software for selecting the relevant action mode for the person during the rider’s practice. Thus, the selected behavior of the horse can be simulated and the injuries of horse-back rider can be avoided. For this purpose, the model of horse-back rider, taking into account its training level and the horse motion, is required. The model of “person – simulation machine” combination is proposed in the article. The proposed model allows developing operating modes taking into account the sportsman-training machine interaction. The mechanical model is an exosuit with a mobile pole, consisting of four links, the rider’s feet, shins, hips, and the corps are attached to. The pole corresponds to the mass center of the horse, the rider interacts with by standing on the stirrups. The pole motion is implemented by a telescopic link attached to immobile base. The relative rotations of the links are implemented by cylindrical hinges with negligible friction. The proposed model has been implemented as software in the “Wolfram Mathematica 11.3” environment. It has been designed for training machine dynamics simulation of the “horse ­– rider” system. The software includes several modules: 1) the module for specifying the structure of training machine mathematical model, generalized coordinates, and for auto-compilation of the corresponding system of differential equations; 2) the module for specifying the programmed model motion and calculation of the required control torques in the hinges; 3) the module for the Cauchy problem numerical solution; 4) the module for the animated visualizing of the model motion, and for exporting the obtained graphic results and numerical calculations. The developed software allows conducting dynamics analysis of mathematical model for the considered system based on the solution of both direct and inverse dynamics problems. Also it can be suggested for designing training machines with programmed operation mode. It has been shown that application of this software accelerates the development of training machines.