Brachistochrone on a velodrome. (24th June 2020)
- Record Type:
- Journal Article
- Title:
- Brachistochrone on a velodrome. (24th June 2020)
- Main Title:
- Brachistochrone on a velodrome
- Authors:
- Benham, G. P.
Cohen, C.
Brunet, E.
Clanet, C. - Abstract:
- Abstract : The Brachistochrone problem, which describes the curve that carries a particle under gravity in a vertical plane from one height to another in the shortest time, is one of the most famous studies in classical physics. There is a similar problem in track cycling, where a cyclist aims to find the trajectory on the curved sloping surface of a velodrome that results in the minimum lap time. In this paper, we extend the classical Brachistochrone problem to find the optimum cycling trajectory in a velodrome, treating the cyclist as an active particle. Starting with two canonical cases of cycling on a sloping plane and a cone, where analytical solutions are found, we then solve the problem numerically on the reconstructed surface of the velodrome in Montigny le Bretonneux, France. Finally, we discuss the parameters of the problem and the effects of fatigue.
- Is Part Of:
- Proceedings. Volume 476:Number 2238(2020)
- Journal:
- Proceedings
- Issue:
- Volume 476:Number 2238(2020)
- Issue Display:
- Volume 476, Issue 2238 (2020)
- Year:
- 2020
- Volume:
- 476
- Issue:
- 2238
- Issue Sort Value:
- 2020-0476-2238-0000
- Page Start:
- Page End:
- Publication Date:
- 2020-06-24
- Subjects:
- brachistochrone -- cycling -- active particles -- optimization
Physical sciences -- Periodicals
Engineering -- Periodicals
Mathematics -- Periodicals
500 - Journal URLs:
- https://royalsocietypublishing.org/loi/rspa ↗
- DOI:
- 10.1098/rspa.2020.0153 ↗
- Languages:
- English
- ISSNs:
- 1364-5021
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD Digital store
- Ingest File:
- 16355.xml