Sliding with Friction and The Brachistochrone Problem

Alexander Kurilin

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arXiv · 2501.18622

Sliding with Friction and The Brachistochrone Problem

Alexander Kurilin

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Abstract

We analyze the motion of a particle in the gravity field along a family of differentiable curves taking into account the Coulomb friction forces. A parametric equation of the optimal curves is given that generalizes the cycloid one in this case. The results of numerical calculations in the Mathcad program show that the found curve minimize the descent time for a given friction coefficient and can claim to be a brachistochrone with Coulomb friction.

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Alexander Kurilin. 2025-01-26. Sliding with Friction and The Brachistochrone Problem. https://arxiv.org/abs/2501.18622

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