Brachistochrone on a velodrome
The Brachistochrone problem, which describes the curve that carries a particle under gravity in
a vertical plane from one height to another in the fastest 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 a recent paper [3], I extended 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 were found, I then solved the problem
numerically on the reconstructed surface of Velodrome de Montigny le Bretonneux in France, comparing with real cyclist data.
[3] Benham, G.P., Cohen, C., Brunet, E., Clanet, C. Brachistochrone on a velodrome. Proceedings of the Royal Society A (2020).
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