Application of the principle of the Pontryagin maximum in the solution of a problem of minimum time

In the present work, necessary and sufficient optimality conditions are presented for the solution to a mínimum time problem. These conditions are established by the principle of the Pontryagin maximum, as a necessary and sufficient condition. In addition, the principle of the Pontryagin maximum is used in the search for the solution to an optimal control problem of mechanical origin.