Geodesic
On control problems of minimum time for Lagrangian systems similar to a swing. I. Convexity criteria for sets
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 5 (1994) no. 3, pp. 247-254

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

One establishes some convexity criteria for sets in \( R^{2} \). They will be applied in a further Note to treat the existence of solutions to minimum time problems for certain Lagrangian systems referred to two coordinates, one of which is used as a control. These problems regard the swing or the ski. 
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     title = {On control problems of minimum time for {Lagrangian} systems similar to a swing. {I.} {Convexity} criteria for sets},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
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Bressan, Aldo; Motta, Monica. On control problems of minimum time for Lagrangian systems similar to a swing. I. Convexity criteria for sets. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 5 (1994) no. 3, pp. 247-254. http://geodesic.mathdoc.fr/item/RLIN_1994_9_5_3_a5/