Does Newtonian dynamics need Euclidean space?

Fuente: arXiv
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Main Author: Albouy, Alain
Format: Preprint
Published: 2025
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author Albouy, Alain
author_facet Albouy, Alain
contents We present an elementary deduction of the Newtonian force from Kepler's laws. We relate it to a generalization by Jacobi of the Keplerian motion, where the Euclidean form in the plane is replaced by some function with the same homogeneity. We show how several convexity properties of the generalized Keplerian orbits appear in this context. We describe the generalized hodographs.
format Preprint
id arxiv_https___arxiv_org_abs_2506_00086
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Does Newtonian dynamics need Euclidean space?
Albouy, Alain
Classical Physics
70F05 (Primary) 26B25 (Secondary)
We present an elementary deduction of the Newtonian force from Kepler's laws. We relate it to a generalization by Jacobi of the Keplerian motion, where the Euclidean form in the plane is replaced by some function with the same homogeneity. We show how several convexity properties of the generalized Keplerian orbits appear in this context. We describe the generalized hodographs.
title Does Newtonian dynamics need Euclidean space?
topic Classical Physics
70F05 (Primary) 26B25 (Secondary)
url https://arxiv.org/abs/2506.00086