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
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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.
@article{RLIN_1994_9_5_3_a5,
author = {Bressan, Aldo and Motta, Monica},
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},
pages = {247--254},
publisher = {mathdoc},
volume = {Ser. 9, 5},
number = {3},
year = {1994},
zbl = {0814.70019},
mrnumber = {MR1298268},
language = {en},
url = {http://geodesic.mathdoc.fr/item/RLIN_1994_9_5_3_a5/}
}
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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/