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) |
---|---|
Pages (from-to) | 383-390 |
Number of pages | 8 |
Journal | Physica D: Nonlinear Phenomena |
Volume | 24 |
Issue number | 1-3 |
DOIs | |
State | Published - 1987 |
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics