On numerical continuation of families of periodic orbits in a parametric potential
type: Item
instance of: scholarly article
title: On numerical continuation of families of periodic orbits in a parametric potential
zbMATH Open document ID: 0873.58036
DOI: 10.1016/0093-6413(96)00025-0
published in: Mechanics Research Communications
publication date: 1997-11-06T00:00:00Z
review text: The author studies the problem of continuing numerically families of periodic orbits in a conservative dynamical systems with two degrees of freedom with respect to one of the parameters of a multiparametric potential. Following the methods and results of \textit{A. Deprit} and \textit{J. Henrard} [Astron. J. 72, 158-172 (1967; per bibl.)] who split the tangent displacement along the orbit from the normal one in variational equations the author obtains a tangent predictor valid for any kind of multiparametric potential function. As an illustration of the method proposed he considers an example of a galactic-type potential in the form of power series with respect to the parameter and Vinti's problem in artificial satellite theory.
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 70F15
zbMATH DE Number: 980285
zbMATH Keywords: parametric potential
zbMATH Keywords: perturbation methods
zbMATH Keywords: periodic orbits
zbMATH Keywords: conservative dynamical systems
zbMATH Keywords: satellite theory
author: Martín Lara
reviewed by: Stanisław Janeczko
MaRDI profile type: Publication
full work available at URL: 0093-6413(96)00025-0
OpenAlex ID: W2023499071
description: scientific article; zbMATH DE number 980285