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UDC 004.942

MODELING OF PARACHUTIST MOVEMENT ON OPEN PARACHUTE

S. S. Mamonov, Dr. Sc. (Phys. and Math.), Head of the Department, RSU, Ryazan; This email address is being protected from spambots. You need JavaScript enabled to view it.
I. U. Klochkova, teacher of the Department, RVVDKU, post-graduate student, RSU, Ryazan; This email address is being protected from spambots. You need JavaScript enabled to view it.

We consider a mathematical model describing the fourth stage of parachutist jump – the decline of open parachute. The aim of the article is to create the system of differential equations, which describes the trajectory of a parachutist as accurately as possible, based on real data of three jumps obtained with the help of a special program installed on the mobile device of parachutists. The original system of differential equations defines the relation between the acceleration of a skydiver from the speed for each of the three coordinates of space. The coefficients of this system of differential equations are obtained by means of regression analysis. The composed system of differential equations is investigated on the basis of stable equilibrium states. On the basis of the obtained equilibrium states, a comparison of real landing speed of a parachutist and a
theoretical one is made, conclusions are drawn. As a result of transformations, the system of differential equations describing the dependence of three coordinates on parachutist's speed is obtained. On the basis of the received system a theoretical trajectory of a parachutist is constructed, its comparison with actual trajectory is carried out, conclusions are drawn.

Key words: mathematical model of parachutist jump, regression analysis, equilibrium state, skydiver trajectory, correlation coefficient, parachutist trajectory, skydiver landing speed.

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