t is too severe and the system has damping,
    then it may be impossible to swing up to the top.  The existence of a
    solution, and number of pumps required to reach the top, is a non-trivial
    function of the initial conditions and the torque-limits.</p>

    <p>Although this system is very simple, obtaining a solution with
    general-purpose algorithms requires much of the same reasoning necessary for
    controlling much more complex underactuated systems; this problem will be a
    work-horse for