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Zbl 0607.70027
Moon, F.C.; Cusumano, J.; Holmes, P.J.
Evidence for homoclinic orbits as a precursor to chaos in a magnetic pendulum. (English)
[J] Physica D 24, 383-390 (1987). ISSN 0167-2789

Experimental evidence is presented which supports the theory that homoclinic orbits in a Poincaré map associated with a phase space flow are precursors of chaotic motion. A permanent magnet rotor in crossed steady and time-varying magnetic fields is shown to satisfy a set of third order differential equations analogous to the forced pendulum or to a particle in a combined periodic and traveling wave force field. Critical values of magnetic torque and forcing frequency are measured for chaotic oscillations of the rotor and are found to be consistent with a lower bound for the existence of homoclinic orbits derived by the method of Melnikov. The fractal nature of the strange attractor is revealed by a Poincaré map triggered by the angular position of the rotor. Numerical simulations using the model also agree well with both theoretical and experimental criteria for chaos.

MSC 2000:: *70K50 Transition to stochasticity (general mechanics)
70K05 Phase plane analysis (general mechanics)
37-99 Dynamic systems and ergodic theory
37D45 Strange attractors, chaotic dynamics

Keywords: homoclinic orbits; Poincaré map; phase space flow; magnet rotor; time- varying magnetic fields; forced pendulum; traveling wave force field; chaotic oscillations; existence of homoclinic orbits; method of Melnikov; fractal nature; strange attractor; Numerical simulations

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Zentralblatt MATH Berlin [Germany]