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Double autoresonance in two-dimensional dynamical systems.

U Rokni1, L Friedland

  • 1Racah Institute of Physics, Hebrew University of Jerusalem, 91904 Jerusalem, Israel.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
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Double autoresonance in two-degree-of-freedom dynamical systems is explored. Under specific conditions, continuous excitation and circular oscillations occur due to frequency changes, demonstrating robust autoresonance.

Area of Science:

  • * Physics
  • * Nonlinear Dynamics
  • * Classical Mechanics

Background:

  • * Explores double autoresonance in dynamical systems with two degrees of freedom.
  • * Analyzes particle motion in a 2D centrally symmetric potential.
  • * Investigates response to a homogeneous quasiperiodic external field with elliptical polarization.

Purpose of the Study:

  • * To examine the phenomenon of double autoresonance.
  • * To analyze particle motion under specific potential and field conditions.
  • * To understand the conditions for the persistence of autoresonance.

Main Methods:

  • * Theoretical analysis of particle motion in a 2D potential.
  • * Investigation of dynamical systems with two degrees of freedom.

Related Experiment Videos

  • * Study of quasiperiodic external fields with elliptical polarization.

    • Main Results:

    • * Double resonance is established for particles with small initial energy as driving frequency approaches linear resonance frequency.
    • * Double resonance persists with further frequency changes, leading to continuous oscillator excitation.
    • * Nonlinearity causes the motion to transform into nearly circular oscillations.

    Conclusions:

    • * Double autoresonance is a key phenomenon in the studied dynamical systems.
    • * The study details the conditions necessary for autoresonance persistence.
    • * Findings contribute to understanding energy transfer and motion control in nonlinear systems.