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The brachistochrone problem with frictional forces

Published online by Cambridge University Press:  15 August 2002

Roberto Giambò  and
Fabio Giannoni
Roberto Giambò
Affiliation:
Dipartimento di Matematica “Ulisse Dini”, Università di Firenze, Italy; giambo@udini.math.unifi.it.
Fabio Giannoni
Affiliation:
Dipartimento di Matematica e Fisica, Università di Camerino, Italy; giannoni@campus.unicam.it.
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Abstract

In this paper we show the existence of the solution for theclassical brachistochrone problem under the action of aconservative field in presence of frictional forces. Assuming thatthe frictional forces and the potential grow at mostlinearly, we prove the existence of a minimizer on the traveltime between any two given points, whenever the initial velocityis great enough. We also prove the uniqueness of the minimizerwhenever the given points are sufficiently close.

Keywords

Minimal travel timenon linear constraints.

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 5 , 2000 , pp. 187 - 206
Copyright
© EDP Sciences, SMAI, 2000

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References

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