Parametric resonance and geodesics on an ellipsoid
type: Item
instance of: scholarly article
title: Parametric resonance and geodesics on an ellipsoid
zbMATH Open document ID: 0811.34039
DOI: 10.1007/BF01075636
publication date: 1994-07-06T00:00:00Z
review text: Let a material point of mass \(m\) move on the line in the field with potential \({k(t) \over 2} x^ 2\), where \(k(t)\) is a positive periodic function of time. The main result gives the answer to the question: for which \(k(t)\), the equilibrium in this system is stable for all sufficiently small \(m\). The answer turns out to be closely related to the Jacobi problem about geodesics on an ellipsoid.
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 70J40
zbMATH DE Number: 571848
zbMATH Keywords: parametric resonance
zbMATH Keywords: potential
zbMATH Keywords: equilibrium
zbMATH Keywords: stable
zbMATH Keywords: geodesics on an ellipsoid
author: A. P. Veselov
reviewed by: Yuri A. Brudnyi
MaRDI profile type: Publication
cites work: Q3042492
cites work: Geodesics on quadrics and a mechanical problem of C. Neumann.
full work available at URL: https://doi.org/10.1007/bf01075636
OpenAlex ID: W2068911538
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 571848