## Abstract

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 field 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 travelling 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.

Original language | English (US) |
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Pages (from-to) | 383-390 |

Number of pages | 8 |

Journal | Physica D: Nonlinear Phenomena |

Volume | 24 |

Issue number | 1-3 |

DOIs | |

State | Published - Jan 1 1987 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics