THE POINT CHARGE OSCILLATOR: QUALITATIVE AND ANALYTICAL INVESTIGATIONS

• Published in: Mathematical modelling and analysis Vol. 24; no. 3; pp. 372 - 384
• Main Author: Schneider, Klaus R.
• Format: Journal Article
• Language: English
• Published: Vilnius Vilnius Gediminas Technical University 01.04.2019
• Subjects: amplitude-period relation; Amplitudes; closed orbits; Elliptic functions; global phase portrait; Infinity; Jacobi elliptic function; Mathematical models; Orbits; Oscillators; Point charge; point charge oscillator; Qualitative analysis; Qualitative research; Germany

We study the mathematical model of the point charge oscillator which has been derived by A. Beléndez et al. [2]. First we determine the global phase portrait of this model in the Poincaré disk. It consists of a family of closed orbits surrounding the unique finite equilibrium point and of a continuu...