This contribution proposes an algorithm to minimise power consumption of electrical vehicles equipped with a permanent magnet three-phase synchronous motor. A constrained optimization problem is formulated and its solution is numerically approximated by using a Hamiltonian function. The problem is posed as a two-point boundary value optimization problem that clearly takes the structural physical constraints and the properties of the system into account. In this optimisation problem the load is considered in terms of the dynamics of the vehicle. In so doing, with the help of a Hamiltonian function consisting of state and costate variables, the optimal solution is directly calculated using a numerical approach. This paper verifies the efficacy of the suggested method by means of simulations of a synchronous motor used in automotive applications.