  In this work, we model the movement of a figure skater gliding on ice by the
Chaplygin sleigh, a classic pedagogical example of a nonholonomic mechanical
system. The Chaplygin sleigh is controlled by a movable added mass, modeling
the movable center of mass of the figure skater. The position and velocity of
the added mass act as controls that can be used to steer the skater in order to
produce prescribed patterns. For any piecewise smooth prescribed curve, this
model can be used to determine the controls needed to reproduce that curve by
approximating the curve with circular arcs. Tracing of the circular arcs is
exact in our control procedure, so the accuracy of the method depends solely on
the accuracy of approximation of a trajectory by circular arcs. To reproduce
the individual elements of a pattern, we employ an optimization algorithm. We
conclude by reproducing a classical "double flower" figure skating pattern and
compute the resulting controls.
