# The brachistochrone problem with frictional forces

Roberto Giambò; Fabio Giannoni

ESAIM: Control, Optimisation and Calculus of Variations (2000)

- Volume: 5, page 187-206
- ISSN: 1292-8119

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top## How to cite

topGiambò, Roberto, and Giannoni, Fabio. "The brachistochrone problem with frictional forces." ESAIM: Control, Optimisation and Calculus of Variations 5 (2000): 187-206. <http://eudml.org/doc/90566>.

@article{Giambò2000,

author = {Giambò, Roberto, Giannoni, Fabio},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {minimal travel time; non linear constraints; brachistochrone problem},

language = {eng},

pages = {187-206},

publisher = {EDP Sciences},

title = {The brachistochrone problem with frictional forces},

url = {http://eudml.org/doc/90566},

volume = {5},

year = {2000},

}

TY - JOUR

AU - Giambò, Roberto

AU - Giannoni, Fabio

TI - The brachistochrone problem with frictional forces

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2000

PB - EDP Sciences

VL - 5

SP - 187

EP - 206

LA - eng

KW - minimal travel time; non linear constraints; brachistochrone problem

UR - http://eudml.org/doc/90566

ER -

## References

top- [1] H. Brezis, Analyse fonctionnelle. Masson, Paris ( 1983). Zbl0511.46001MR697382
- [2] F. Giannoni, P. Piccione and J.A. Verderesi, An approach to the relativistic brachistochrone problem by sub-Riemannian geometry. J. Math. Phys. 38 ( 1997) 6367-6381. Zbl0897.53051MR1483499
- [3] F. Giannoni and P. Piccione, An existence theory for relativistic brachistochrones in stationary space-times. J. Math. Phys. 39 ( 1998) 6137-6152. Zbl0934.58016MR1653097
- [4] J. Nash, The embedding problem for Riemannian manifolds. Ann. Math. 63 ( 1956) 20-63. Zbl0070.38603MR75639
- [5] L.A. Pars, An Introduction to the Calculus of Variations. Heinemann, London ( 1962). Zbl0108.10303MR147932
- [6] V. Perlick, The brachistochrone problem in a stationary space-time. J. Math. Phys. 32 ( 1991) 3148-3157. Zbl0771.49018MR1131701

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