Analytical solutions for a nonlinear coupled pendulum

Authors:
Ligia Munteanu;Veturia Chiroiu;Stefania Donescu
Affiliations:
Institute of Solid Mechanics of Romanian Academy, Bucharest;Institute of Solid Mechanics of Romanian Academy, Bucharest;Technical University of Civil Engineering, Bucharest
Venue:
MACMESE'08 Proceedings of the 10th WSEAS international conference on Mathematical and computational methods in science and engineering
Year:
2008

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Abstract

In this paper, the motion of two pendulums coupled by an elastic spring is studied. By extending the linear equivalence method (LEM), the solutions of its simplified set of nonlinear equations are written as a linear superposition of Coulomb vibrations. The inverse scattering transform is applied next to exact set of equations. By using the Θ - function representation, the motion of pendulum is describable as a linear superposition of cnoidal vibrations and additional terms, which include nonlinear interactions among the vibrations. Comparisons between the LEM and cnoidal solutions and comparisons with the solutions obtained by the fourth-order Runge-Kutta scheme are performed. Finally, an interesting phenomenon is put into evidence with consequences for dynamic of pendulums.