  We solve the problem concerning a time optimal return of a particle with a
prescribed velocity to the origin by applying a magnitude-bounded force. The
equations of controlled motion are derived and explicitly integrated, and the
optimal open-loop control and optimal time are analyzed depending on the
parameters of the problem. The qualitative behavior of the solution is
established, and the solution is compared with other regimes of motion. The
results are of interest for control theory and its applications to controlled
flight mechanics.
