Traveling Wave Solutions For Newton's Equations of Celestial Mechanics: Kepler's Problem
Mathematical Physics
2024-05-24 v1 Classical Analysis and ODEs
Dynamical Systems
math.MP
Abstract
This article produces wave equations and constructs traveling wave solutions that are intimately related to Newton's equations of celestial mechanics. The traveling wave solutions are expressed in ``closed form'' in terms of elementary functions. They are specialized to the 2-body and the relative 2-body problem. The traveling wave solutions disclose the shape and position of wave fronts emanating from collisions by determining the location of the singularities of the traveling wave solutions.
Keywords
Cite
@article{arxiv.2405.13262,
title = {Traveling Wave Solutions For Newton's Equations of Celestial Mechanics: Kepler's Problem},
author = {Harry Gingold and Jocelyn Quaintance},
journal= {arXiv preprint arXiv:2405.13262},
year = {2024}
}
Comments
18 pages, 8 figures