The brachistochrone problem with frictional forces

Free access article

Issue		ESAIM: COCV Volume 5, 2000


Page(s)		187 - 206
DOI		10.1051/cocv:2000107

DOI: 10.1051/cocv:2000107

ESAIM: COCV, March 2000, Vol. 5, p. 187-206

The brachistochrone problem with frictional forces

Roberto Giambò
Dipartimento di Matematica "Ulisse Dini'', Università di Firenze, Italy; (giambo@udini.math.unifi.it)

Fabio Giannoni
Dipartimento di Matematica e Fisica, Università di Camerino, Italy; (giannoni@campus.unicam.it)

Received October 1, 1999.

Abstract: In this paper we show the existence of the solution for the classical brachistochrone problem under the action of a conservative field in presence of frictional forces. Assuming that the frictional forces and the potential grow at most linearly, we prove the existence of a minimizer on the travel time between any two given points, whenever the initial velocity is great enough. We also prove the uniqueness of the minimizer whenever the given points are sufficiently close.

Keywords and phrases: Minimal travel time, non linear constraints.

AMS Subject Classification: 58E30, 58E25, 45J05.

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