Volume 5, 2000
|Page(s)||187 - 206|
|Published online||15 August 2002|
The brachistochrone problem with frictional forces
Dipartimento di Matematica “Ulisse Dini”,
Università di Firenze, Italy;
2 Dipartimento di Matematica e Fisica, Università di Camerino, Italy; email@example.com.
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.
Mathematics Subject Classification: 58E30 / 58E25 / 45J05
Key words: Minimal travel time / non linear constraints.
© EDP Sciences, SMAI, 2000
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.