Qualitative Theory of Dynamical Systems

, Volume 12, Issue 1, pp 115–139

2-D Duffing Oscillator: Elliptic Functions from a Dynamical Systems Point of View

  • Francisco Javier Molero
  • Martín Lara
  • Sebastián Ferrer
  • Francisco Céspedes
Article

DOI: 10.1007/s12346-012-0081-1

Cite this article as:
Molero, F.J., Lara, M., Ferrer, S. et al. Qual. Theory Dyn. Syst. (2013) 12: 115. doi:10.1007/s12346-012-0081-1

Abstract

K. Meyer has advocated for the study of elliptic functions and integrals from a dynamical systems point of view. Here, we follow his advice and we propose the bidimensional Hamiltonian Duffing oscillator as a model; it allows us to deal with the elliptic integral of third kind directly. Focusing on bounded trajectories we do a detailed analysis of the solutions in the three regions defined by the parameters. In our opinion, for the study of elliptic functions, the model presented here represents an alternative to the pendulum or the free rigid body systems.

Keywords

Integrable systems Hamiltonian systems Duffing oscillator Jacobi elliptic functions Elliptic integrals Elliptic integral of the third kind 

Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  • Francisco Javier Molero
    • 1
  • Martín Lara
    • 1
  • Sebastián Ferrer
    • 1
  • Francisco Céspedes
    • 1
  1. 1.Departamento de Matemática AplicadaUniversidad de MurciaEspinardo, MurciaSpain