• Media type: Text; E-Book; Report
  • Title: The point charge oscillator: Qualitative and analytical investigations
  • Contributor: Schneider, Klaus R. [Author]
  • imprint: Weierstrass Institute for Applied Analysis and Stochastics publication server, 2018
  • Language: English
  • DOI: https://doi.org/10.20347/WIAS.PREPRINT.2536
  • Keywords: article ; 34C27 ; 78A35 ; Global phase portrait -- closed orbits -- homoclinic orbits -- amplitude-period relation -- Jacobi elliptic function ; 34C05 ; 34C15
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  • Description: We 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 perod Τα of the oscillation with the amplitude α as α tends to infinity. Finally, we determine an exact relation between period and amplitude by means of the Jacobi elliptic function cn.