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minimal travel time

ESAIM: Control, Optimisation and Calculus of Variations (1)

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The brachistochrone problem with frictional forces
Roberto Giambò, Fabio Giannoni
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 5 / 2000

Published online by Cambridge University Press:

15 August 2002, pp. 187-206

Print publication:

2000
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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.