Limiting Cases of Impulsive Manipulation

Impulsive manipulation is the use of impulsive forces to manipulate objects. In particular, we are studying how tomanipulate a rigid planar slider by tapping. In this paper, we focus on the limiting case — where the number of taps approaches infinity as the energy of each tap approaches zero. This paper develops two definitions of the limiting case: for intermittent tapping, where the object comes to rest between taps, and for continuous tapping, where the object does not come to rest. For intermittent tapping, we find that the motion obeys a simple scaling law, and for continuous tapping, we find that there is a limiting case such that the possible motions of the object are identical to those for pushing for rotationally symmetric objects. We also explore analogous forms of vibratory manipulation, where we take the striker behavior foremost and examine the resulting object motion.