Computing planar and spherical choreographies

Hadrien Montanelli; Nikola I. Gushterov

doi:10.1137/15M1024652

Computing planar and spherical choreographies

Hadrien Montanelli
, Nikola I. Gushterov

University of Oxford

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	235-256
Number of pages	22
Journal	SIAM Journal on Applied Dynamical Systems
Volume	15
Issue number	1
DOIs	https://doi.org/10.1137/15M1024652
Publication status	Published - 1 Jan 2016
Externally published	Yes

Keywords

Choreographies
N-body problem
Newton's Method
Quasi-Newton methods
Trigonometric interpolation

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10.1137/15M1024652

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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.",

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AB - 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.

KW - Choreographies

KW - N-body problem

KW - Newton's Method

KW - Quasi-Newton methods

KW - Trigonometric interpolation

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JF - SIAM Journal on Applied Dynamical Systems

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Computing planar and spherical choreographies

Abstract

Keywords

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