UDC 004.942
I. Y. Klochkova, teacher of the department, Ryazan Guards Higher Airborne Command School, Ryazan, Russia;
orcid.org/0000-0002-4265-6759, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
A mathematical model of parachutist movement describing the stage of descent on open parachute is considered.
The aim of the work is to study the system of ordinary differential equations describing the speed of
parachutist movements for the presence and stability of equilibrium states. Initially, the system of differential
equations determines the relationship between the acceleration of parachute and the velocity for each
of three space coordinates. Various variations of this system of differential equations are considered. Theorems
on the number and stability of equality states are proved.
Numerical coefficients values for the system of differential equations based on real data of jumps obtained
using a special program installed on parachutist mobile device by regression analysis method are
obtained. The equilibrium states for each jump, their stability, practical significance and maximum value of
the speed at the time of landing are determined. Theoretical parachutist trajectory for the obtained system of
differential equation is constructed; its comparison with actual trajectory is carried out.
Key words: mathematical model of parachutist movement, equilibrium state, regression analysis, correlation
coefficient, parachutist trajectory, parachutist landing speed.