To the theory of motion of bodies with variable mass

In previous papers, a new approach has been proposed for describing the dynamics of nonlinear motion of material bodies with account for dry and viscous friction, which is based on the following steps: formulation of the corresponding dynamic equations in the single orthogonal moving basis formed by unit normal vectors and a tangent, which are drawn at a given trajectory point with the tangent vector directed along the body; and an assumption that in the framework of nonlinear motion along a brachistochrone, the reaction force can be specified analytically only.
Having applied this approach, the problem on the description of the dynamics of motion of variable-mass bodies at a given mass variation law is solved in this paper. A set of simultaneous dynamic equations is obtained to parametrically describe the point particle motion. Based on the numerical solution of these equations, three types of brachistochrone are plotted for desired mass variation laws, and their significant difference from the constant-mass case is shown.