Radial stability of periodic orbits of damped Keplerian-like systems
type: Item
instance of: scholarly article
title: Radial stability of periodic orbits of damped Keplerian-like systems
zbMATH Open document ID: 1436.34038
author: Zaitao Liang
author: Fang-Fang Liao
published in: Nonlinear Analysis. Real World Applications
publication date: 2020-04-15T00:00:00Z
review text: The authors prove some stability results for planar systems of the type \[ \ddot x + h(t) \dot x + g(t) \frac{x}{|x|^{\alpha+1}}=0\,, \] where \(\alpha>0\), \(g,h:{\mathbb R}\to{\mathbb R}\) are continuous and \(T\)-periodic functions, with \[ \bar h:=\frac{1}{T}\int_0^T h(t)\,dt=0. \] Their aim is to establish some sufficient conditions for the existence of radially T-periodic collisionless solutions \(x:{\mathbb R}\to{\mathbb R}^2\setminus\{0\}\) which are Lyapunov stable in the radial direction. The results are new also for the Kepler problem, with \(h\equiv0\) and \(\bar g>0\).
reviewed by: Alessandro Fonda
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 70M20
Mathematics Subject Classification ID: 37C60
zbMATH DE Number: 7189397
zbMATH Keywords: Keplerian-like systems
zbMATH Keywords: periodic orbits
zbMATH Keywords: radial stability
zbMATH Keywords: twist
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2020.103093
OpenAlex ID: W3003354173
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DOI: 10.1016/J.NONRWA.2020.103093
description: scientific article; zbMATH DE number 7189397