On a generalization of Lissajous curves and its applications
Piotr Krasoń, Jan Milewski, Wojciech Bondarewicz, Aleksandra Wojtaszek
Banach Center Publications 109 (2016), 83-98
MSC: Primary 14H50; Secondary 14H81; 83C10; 30F30; 53A35; 70B05; 83C20.
DOI: 10.4064/bc109-0-6
Streszczenie
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.
Autorzy
- Piotr KrasońDepartment of Mathematics and Physics
University of Szczecin
Wielkopolska 15
70-415 Szczecin, Poland
e-mail
- Jan MilewskiInstitute of Mathematics
Poznań University of Technology
Piotrowo 3A
60-965 Poznań, Poland
e-mail
- Wojciech BondarewiczDepartment of Mathematics and Physics
University of Szczecin
Wielkopolska 15
70-415 Szczecin, Poland
e-mail
- Aleksandra WojtaszekThe Department of CRM and Sales Support
Bank Zachodni WBK SA
Plac Andersa 5
61-894 Poznań, Poland
e-mail