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

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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.

langue originale	Anglais
Pages (de - à)	235-256
Nombre de pages	22
journal	SIAM Journal on Applied Dynamical Systems
Volume	15
Numéro de publication	1
Les DOIs	https://doi.org/10.1137/15M1024652
état	Publié - 1 janv. 2016
Modification externe	Oui

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10.1137/15M1024652

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title = "Computing planar and spherical choreographies",

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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DO - 10.1137/15M1024652

M3 - Article

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JF - SIAM Journal on Applied Dynamical Systems

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Computing planar and spherical choreographies

Résumé

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