  We study the minimum time control problem of the launchers. The optimal
trajectories of the problem may contain singular arcs, and thus chattering
arcs. The motion of the launcher is described by its attitude kinematics and
dynamics and also by its trajectory dynamics. Based on the nature of the
system, we implement an efficient indirect numerical method, combined with
numerical continuation, to compute numerically the optimal solutions of the
problem. Numerical experiments show the efficiency and the robustness of the
proposed method.
