modeling of flight of the line thrower projectile

The actual problem of increasing the flight range of line thrower projectile which is a container with a line (thin rope) inside. the line leaves the container during the flight, i.e. the projectile has a variable mass. mathematical model of the projectile flight is constructed using the lagrange equations of the second kind. the projectile is considered as a material particle, the line considered as an elastic thread with the tensile cauchy strain. an approximation of the projectile flight trajectory is introduced in terms of three generalized coordinates. the dependence of the projectile’s flight distance on the projectile departure angle is constructed for several values of the tensile rigidity of the line.