Sliding with Friction and The Brachistochrone Problem
Classical Physics
2025-02-03 v1
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.
Keywords
Cite
@article{arxiv.2501.18622,
title = {Sliding with Friction and The Brachistochrone Problem},
author = {Alexander Kurilin},
journal= {arXiv preprint arXiv:2501.18622},
year = {2025}
}
Comments
18 pages, 7 figures