• DOI:10.4064/BC109-0-6
• Corpus ID: 55328010

On a generalization of Lissajous curves and its applications

@article{Kraso2016OnAG,
  title={On a generalization of Lissajous curves and its applications},
  author={Piotr Krasoń and Jan Milewski and Wojciech Bondarewicz and Aleksandra Wojtaszek},
  journal={Banach Center Publications},
  year={2016},
  volume={109},
  pages={83-98}
}

• P. Krasoń, J. Milewski, +1 author Aleksandra Wojtaszek
• Published 2016
• Mathematics
• Banach Center Publications

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. 2010 Mathematics Subject Classification: Primary 14H50; Secondary 14H81; 83C10; 30F30; 53A35; 70B05; 83C20.