How to build a new athletic track to break records

Amandine Aftalion (1) , Emmanuel Trélat (2, 3)

1 CAMS - Centre d'Analyse et de Mathématique sociales
2 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
3 CaGE - Control And GEometry

We introduce a new optimal control model which encompasses pace optimization and motor control effort for a runner on a fixed distance. The system couples mechanics, energetics, neural drive to an economic decision theory of cost and benefit. We find how effort is minimized to produce the best running strategy, in particular in the bend. This allows us to discriminate between different types of tracks and estimate the discrepancy between lanes. Relating this model to the optimal path problem called the Dubins path, we are able to determine the geometry of the optimal track and estimate record times.

Domaines: Optimisation et contrôle [math.OC]

Amandine Aftalion, Emmanuel Trélat. How to build a new athletic track to break records. Royal Society Open Science, 2020, 7 (200007), pp.10. ⟨10.1098/rsos.200007⟩. ⟨hal-02441643v2⟩