Consider a body of mass m, acted on by a thrust force. Assume that the magnitude of the force is constant, and the angle is the control variable. The motion is planar, so the governing equations are y1(t) = acos(ut), y1(0) = 0, y2(t) = asin(ut), y2(0) = 0. The goal is to choose the angle u(t) so that 2T is maximized, where T is some fixed time, subject to T > 0 and T = 0. This is the optimal control problem in question 5 from assignment 7. Calculate the Pontryagin Hamiltonian and the optimality equations. Compare with the previously calculated optimality equations.