The point charge oscillator: Qualitative and analytical investigations

dc.bibliographicCitation.firstPage372eng
dc.bibliographicCitation.issue3eng
dc.bibliographicCitation.journalTitleMathematical modelling and analysiseng
dc.bibliographicCitation.lastPage384eng
dc.bibliographicCitation.volume24eng
dc.contributor.authorSchneider, Klaus R.
dc.date.accessioned2022-06-21T10:58:03Z
dc.date.available2022-06-21T10:58:03Z
dc.date.issued2019
dc.description.abstractWe study the mathematical model of the point charge oscillator which has been derived by A. Belendez et al. [2]. First we determine the global phase portrait of this model in the Poincare disk. It consists of a family of closed orbits surrounding the unique finite equilibrium point and of a continuum of homoclinic orbits to the unique equilibrium point at infinity. Next we derive analytic expressions for the relationship between period (frequency) and amplitude. Further, we prove that the period increases monotone with the amplitude and derive an expression for its growth rate as the amplitude tends to infinity. Finally, we determine a relation between period and amplitude by means of the complete elliptic integral of the first kind K(k) and of the Jacobi elliptic function cn.eng
dc.description.versionpublishedVersioneng
dc.identifier.urihttps://oa.tib.eu/renate/handle/123456789/9095
dc.identifier.urihttps://doi.org/10.34657/8133
dc.language.isoengeng
dc.publisherVilnius : Vilnius Gediminas Technical Universityeng
dc.relation.doihttps://doi.org/10.3846/mma.2019.023
dc.relation.essn1648-3510
dc.rights.licenseCC BY 4.0 Unportedeng
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/eng
dc.subject.ddc510eng
dc.subject.ddc050eng
dc.subject.otherAmplitude-period relationeng
dc.subject.otherClosed orbitseng
dc.subject.otherGlobal phase portraiteng
dc.subject.otherJacobi elliptic functioneng
dc.subject.otherPoint charge oscillatoreng
dc.titleThe point charge oscillator: Qualitative and analytical investigationseng
dc.typeArticleeng
dc.typeTexteng
tib.accessRightsopenAccesseng
wgl.contributorWIASeng
wgl.subjectMathematikeng
wgl.typeZeitschriftenartikeleng
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