Deriving friction force using fractional calculus
Mesoscale and Nanoscale Physics
2024-07-22 v1 Mathematical Physics
math.MP
Classical Physics
Abstract
The friction force is derived using fractional calculus by considering the non-uniform flow of time in dissipative processes. The approach incorporates inhomogeneous velocity without unphysical approximations, resulting in a Lagrangian where the order of fractional derivatives measures time intervals. The fractional term in the Lagrangian provides correct Euler-Lagrange, and ultimately, the Hamilton equations, and vanishes during energy change measurements, like a ghost.
Cite
@article{arxiv.2407.13888,
title = {Deriving friction force using fractional calculus},
author = {Georgii Koniukov},
journal= {arXiv preprint arXiv:2407.13888},
year = {2024}
}