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Sliding with Friction and The Brachistochrone Problem

2025/01/26 by Alexander Kurilin, Kurilin, Alexander
Engineering · Neuroscience · #Classical Physics (physics.class-ph) #FOS: Physical sciences #Mechanics and Biomechanics Studies #Motor Control and Adaptation #Tactile and Sensory Interactions

paper · pdf · doi:10.48550/arxiv.2501.18622

openalex publication_date 2025/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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