Trajectory tracing in figure skating

In this work, we model the movement of a figure skater gliding on ice by Chaplygin sleigh, classic pedagogical example nonholonomic mechanical system. The sleigh is controlled movable added mass, modeling center mass skater. position and velocity act as controls that can be used to steer in order produce prescribed patterns. Our control method based observation any piecewise smooth curve approximated collection circular arcs. We impose steering constraint stating contact point moving locally along arc. Then, accuracy depends solely approximation trajectory To reproduce individual elements pattern, employ mechanism minimization square relative subject being conclude reproducing classical “double flower” skating pattern compute resulting controls.