On the chaotic dynamics of a spherical pendulum with a harmonically vibrating suspension

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Author(s)

  • A. Y T Leung
  • J. L. Kuang

Detail(s)

Original languageEnglish
Pages (from-to)213-238
Journal / PublicationNonlinear Dynamics
Volume43
Issue number3
Publication statusPublished - Feb 2006

Abstract

The equations of motion for a lightly damped spherical pendulum are considered. The suspension point is harmonically excited in both vertical and horizontal directions. The equations are approximated in the neighborhood of resonance by including the third order terms in the amplitude. The stability of equilibrium points of the modulation equations in a four-dimensional space is studied. The periodic orbits of the spherical pendulum without base excitations are revisited via the Jacobian elliptic integral to highlight the role played by homoclinic orbits. The homoclinic intersections of the stable and unstable manifolds of the perturbed spherical pendulum are investigated. The physical parameters leading to chaotic solutions in terms of the spherical angles are derived from the vanishing Melnikov-Holmes-Marsden (MHM) integral. The existence of real zeros of the MHM integral implies the possible chaotic motion of the harmonically forced spherical pendulum as a result from the transverse intersection between the stable and unstable manifolds of the weakly disturbed spherical pendulum within the regions of investigated parameters. The chaotic motion of the modulation equations is simulated via the 4th-order Runge-Kutta algorithms for certain cases to verify the analysis. © Springer 2006.

Research Area(s)

  • Bifurcation, Chaos, Equations of modulation, Melnikov-Holmes-Marsden integral, Spherical pendulum

Citation Format(s)

On the chaotic dynamics of a spherical pendulum with a harmonically vibrating suspension. / Leung, A. Y T; Kuang, J. L.
In: Nonlinear Dynamics, Vol. 43, No. 3, 02.2006, p. 213-238.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review