Computing planar and spherical choreographies
arXiv:1505.0484817 citationsh-index: 13
Originality Synthesis-oriented
AI Analysis
For researchers studying choreographies in celestial mechanics, this provides a computational method to find new solutions.
The paper presents an algorithm for computing choreographies in the plane and on the sphere, discovering new choreographies on the sphere.
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.