This paper describes an analytical method of computation of optimal controls which minimize the energy consumption by rail or any other fixed path vehicles. A specific aspect of this problem is that the external forces applied to the vehicle and the maximum allowable speed depend on the coordinate of the vehicle. The known analytical solutions do not take this important feature into account. Classical numerical methods of optimization cannot be used by an on-board computer since they require significant computation time. We applied the maximum principle to determine: the set of optimal controls, the switching graphs and the optimality conditions. Based on these results, we developed an efficient computation algorithm without sacrificing the accuracy of the mathematical model. The paper is concluded with an example of optimal controls and discussion of some applications of the presented method.