  The goal of this paper is to investigate the normal and tangential forces
acting at the point of contact between a horizontal surface and a rolling ball
actuated by internal point masses moving in the ball's frame of reference. The
normal force and static friction are derived from the equations of motion for a
rolling ball actuated by internal point masses that move inside the ball's
frame of reference, and, as a special case, a rolling disk actuated by internal
point masses. The masses may move along one-dimensional trajectories fixed in
the ball's and disk's frame. The dynamics of a ball and disk actuated by masses
moving along one-dimensional trajectories are simulated numerically and the
minimum coefficients of static friction required to prevent slippage are
computed.
