Hadrien Montanelli
University of Oxford
Publications:
Montanelli H.
Computing Hyperbolic Choreographies
2016, vol. 21, no. 5, pp. 522530
Abstract
An algorithm is presented for numerical computation of choreographies in spaces of constant negative curvature in a hyperbolic cotangent potential, extending the ideas given in a companion paper [14] for computing choreographies in the plane in a Newtonian potential and on a sphere in a cotangent potential. Following an idea of Diacu, PérezChavela and Reyes Victoria [9], we apply stereographic projection and study the problem in the Poincaré disk. Using approximation by trigonometric polynomials and optimization methods with exact gradient and exact Hessian matrix, we find new choreographies, hyperbolic analogues of the ones presented in [14]. The algorithm proceeds in two phases: first BFGS quasiNewton iteration to get close to a solution, then Newton iteration for high accuracy.
