On a generalization of Lissajous curves and its applications
Volume 109 / 2016
Banach Center Publications 109 (2016), 83-98
MSC: Primary 14H50; Secondary 14H81; 83C10; 30F30; 53A35; 70B05; 83C20.
DOI: 10.4064/bc109-0-6
Abstract
In the paper we consider a generalization of classical Lissajous curves to the situation where corresponding differential forms involve square roots of quartics. We give a new interesting parametrization of these curves and fully analyze their behaviour in terms of roots of the quartics. We indicate natural applications of our method to the analysis of a Duffing oscillator where the Higgs potential is described by a quartic. We also describe an application to the study of movement of a test body in an axially symmetric gravitational field described by the Kerr metric.
