Symmetric Solutions to Nonlinear Vectorial 2nd Order ODE's
Classical Analysis and ODEs
2021-12-23 v1
Abstract
It is proven that second-order vectorial nonlinear differential systems y''=f(y) , possess a continuum of symmetric solutions. They are shown to possess a continuum of even solutions. If f(y) is an odd function of y , then y''=f(y) is shown also to possess a continuum of odd solutions. The results apply to a significant family of second-order vectorial nonlinear differential systems that are not dissipative. This family of differential equations includes the celebrated N-body problem of celestial mechanics and other central force problems.
Cite
@article{arxiv.2112.11528,
title = {Symmetric Solutions to Nonlinear Vectorial 2nd Order ODE's},
author = {Ali Abdulhussein and Harry Gingold},
journal= {arXiv preprint arXiv:2112.11528},
year = {2021}
}