  Juggling a devil-stick can be described as a problem of non-prehensile
manipulation. Assuming that the devil-stick remains confined to the vertical
plane, the problem of juggling the stick between two symmetric configurations
is considered. Impulsive forces are applied to the stick intermittently and the
impulse of the force and its point of application are modeled as control inputs
to the system. The dynamics of the devil-stick due to the impulsive forces and
gravity is described by half-return maps between two Poincare sections; the
symmetric configurations are fixed points of these sections. A coordinate
transformation is used to convert the juggling problem to that of stabilization
of one of the fixed points. Inclusion of the coordinate transformation in the
dynamic model results in a nonlinear discrete-time system. A dead-beat design
for one of the inputs simplifies the control problem and results in a linear
time-invariant discrete-time system. Standard control techniques are used to
show that symmetric juggling can be achieved from arbitrary initial conditions.
