Computing planar and spherical choreographies
Numerical Analysis
2015-11-19 v4
Abstract
An algorithm is presented for numerical computation of choreographies in the plane in a Newtonian potential and on the sphere in a cotangent potential. It is based on stereographic projection, approximation by trigonometric polynomials, and quasi-Newton and Newton optimization methods with exact gradient and exact Hessian matrix. New choreographies on the sphere are presented.
Cite
@article{arxiv.1505.04848,
title = {Computing planar and spherical choreographies},
author = {Hadrien Montanelli and Nikola Ivanov Gushterov},
journal= {arXiv preprint arXiv:1505.04848},
year = {2015}
}