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Time-Optimal Control Problem for the Swing and the Ski

Benedetto Piccoli
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Abstract

This paper is concerned with a class of time-optimal control problems for the swing and the ski. We first consider the motion of a man standing on a swing. For simplicity, we neglect friction and air resistance and assume that the mass of the swinger is concentrated in his baricenter $B$. For the ski, we use the model considered by Aldo Bressan (1991), with a special approximation of the skier. Our main concern is the existence and the structure of time-optimal controls. As first step, we introduce an auxiliary control system with control entering linearly and show the relationships between this and the original system. We then perform a detailed study of the auxiliary system, using geometric techniques. In turn this provides accurate information on the time-optimal controls for the original system.

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Benedetto Piccoli. 1994-11-03. Time-Optimal Control Problem for the Swing and the Ski. https://arxiv.org/abs/funct-an/9411004

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