Periodic solutions of twist type of an Earth satellite equation.
type: Item
instance of: scholarly article
title: Periodic solutions of twist type of an Earth satellite equation.
zbMATH Open document ID: 1068.70027
author: Pedro J. Torres
author: Daniel E. Nuñez
published in: Discrete and Continuous Dynamical Systems
publication date: 2003-03-16T00:00:00Z
review text: The authors consider the ordinary differential equation of the form \[ x''+\alpha\sqrt{1+\sin^2t}\sin x=6\sin {2t}(1+\sin^2t)^{-2}, \] where \(\alpha\) is a positive physical parameter related to magnetic intensity. The equation is a simple model of the motion of a satellite (a material point) in the orbit around the Earth. Earlier by \textit{A. A. Zevin} and \textit{M. A. Pinsky} [Discrete Contin. Dyn. Syst. 6, No. 2, 293--297 (2000; Zbl 1109.70308)], it was proved that for \(\alpha \leq1/2\) there exists a stable solution (in Lyapunov sense) in the linear case. The goal of this paper is to prove the Lyapunov stability of satellite motion under more restrictive bound on the parameter \(\alpha \leq 1/18\) by the use of some new results on the so-called twist solutions and taking into account the bilateral bounds found in the above-mentioned paper by Zevin and Pinsky.
reviewed by: Sergei Georgievich Zhuravlev
Mathematics Subject Classification ID: 70M20
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 1882978
zbMATH Keywords: Lyapunov stability
MaRDI profile type: Publication
full work available at URL: dcds.2001.7.303
OpenAlex ID: W1993406876
DOI: 10.3934/DCDS.2001.7.303
description: scientific article; zbMATH DE number 1882978