Моделирование влияния ветра на траекторию движения парашютиста

Abstract

The article considers a mathematical model of a parachutist floating on the open parachute in the wind. The aim of the work is to study a system of differential equations describing the speed of the motion of the parachutist when descending on the open parachute, in order to establish the dependence of the trajectory of movement of the parachutist, the presence and stability of equilibrium states on the wind. Initially, a system of ordinary differential equations is considered, which determines the relationship between the acceleration of the parachutist and the speed along each of the three coordinates of space in windless weather. Then the influence of the wind is taken into account. The theorem on the number and stability of equilibrium states is proved. Numerical values of coefficients of the system of differential equations are obtained on the basis of real data received with the help of special software installed on the parachutist's mobile device by the method of nonlinear regression analysis. The equilibrium states of the jump, their stability and the maximum value of the speeds at the moment of landing with the presence of wind are determined. For the obtained system of ordinary differential equations, a theorem is proved on the magnitude of the skydiver's drift, the curvature and torsion of the trajectory depending on the wind.