NDLI: On the Chaotic Dynamics of a Spherical Pendulum with a Harmonically Vibrating Suspension

Content Provider	Springer Nature Link
Author	Leung, A. Y. T. Kuang, J. L.
Copyright Year	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.
Starting Page	213
Ending Page	238
Page Count	26
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	43
Issue Number	3
e-ISSN	1573269X
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2006-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	spherical pendulum bifurcation chaos Melnikov–Holmes–Marsden integral equations of modulation Mechanics Vibration, Dynamical Systems, Control Mechanical Engineering Automotive and Aerospace Engineering, Traffic
Content Type	Text
Resource Type	Article
Subject	Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering

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