Influence of the size of a controllable device on time-optimal rotation generated by a moving internal mass
A two-dimensional time-optimal control problem with a state constraint is studied for a closed mechanical system consisting of a mass point and a solid body that interact via internal forces. It is assumed that the mass point is not allowed to move further away from the body's center of mass than a prescribed distance. A control function is found allowing the body to be turned through a given angle in a minimum time by choosing the velocity of the mass point. In the case of reaching the state constraint, the solution is constructed in explicit form via quadratures representing elliptic integrals. A numerical example of using the derived formulas is given.