Synthesis of a control in the problem of the time-optimal transfer of a point mass to a specified position with zero velocity

The problem of the time-optimal control of the motion of a point mass by means of a force of bounded modulus is considered. It is required that the point be transferred from an arbitrary state of motion to the origin of the system of coordinates with zero velocity. By introducing self-similar conjugate variables, the solution of the two-point problem can be successfully reduced to a search for the optimal root of a certain function, specified analytically. A complete solution of the control problem in the form of a synthesis is obtained using mathematical modelling methods. The feedback coefficients along the unit vectors of the position and velocity vectors are found and a control algorithm and a Bellman function are constructed. Examples using practical initial data are presented.