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

• Francisco Javier Molero ^[1] ; Martín Lara ^[1] ; Sebastián Ferrer ^[1] ; Francisco Céspedes ^[1]
  1. [1] Universidad de Murcia

     Universidad de Murcia

     Murcia, España

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 12, Nº 1, 2013, págs. 115-139
• Idioma: inglés
• DOI: 10.1007/s12346-013-0098-0
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.