This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Schneider, Klaus R.2018-10-112019-06-2820182198-5855https://doi.org/10.34657/3369https://oa.tib.eu/renate/handle/123456789/2706We determine the global phase portrait of a mathematical model describing the point charge oscillator. It shows that the family of closed orbits describing the point charge oscillations has two envelopes: an equilibrium point and a homoclinic orbit to an equilibrium point at infinity. We derive an expression for the growth rate of the primitive period Ta of the oscillation with the amplitude a as a tends to infinity. Finally, we determine an exact relation between period and amplitude by means of the Jacobi elliptic function cn.application/pdfeng510Global phase portraitclosed orbitsamplitude-period relationJacobi elliptic functionReport