Homoclinic orbits in the dynamics of resonantly driven coupled pendula |
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Authors: | Gregor Kovačič Thomas A Wettergren |
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Institution: | (1) Mathematical Sciences Dept, Rensselaer Polytechnic Institute, 12180 Troy, NY;(2) Naval Undersea Warfare Center, Code 8423, 02841 Newport, RI, USA |
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Abstract: | We present a plethora of homoclinic and heteroclinic orbits that exist in the phase space of a weakly nonlinear model describing small oscillations of two resonantly driven coupled pendula. These orbits connect equilibria in a resonance band, which is contained in an invariant plane, and is born under perturbation out of a circle of equilibria. Their existence is shown by using a combination of the Melnikov method and singular perturbation techniques. |
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