In this paper, the authors consider a class of finite dimensional optimal control problems with state restrictions. These investigations are aimed at utilizable necessary optimality conditions. The purpose of the paper is twofold: first, to prepare a starting point for further investigations on a topic from mechanics begun in  and, second, finally to have a written material that can be used in teaching this somewhat unwieldy subject. The optimality conditions are derived by transforming the control problem into a Bolza-type variational problem and then using techniques coming from classical literature in Calculus of Variations. The results are applied to some modified and generalized problems of Dido type. The concluding chapter addresses variational problems and integral principles from Analytical Mechanics under state constraints.