1994/11/03 by Benedetto Piccoli, Piccoli, Benedetto
Earth and Planetary Sciences · Engineering · Mathematics · Medicine · #Cryospheric studies and observations #FOS: Mathematics #Functional Analysis (math.FA) #Stability and Controllability of Differential Equations #Winter Sports Injuries and Performance #funct-an #math.FA
paper · pdf · doi:10.48550/arxiv.funct-an/9411004
26 pages, plain tex, no figures
arxiv created 1994/11/03 · openalex publication_date 1994/11/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.