Physics – Condensed Matter
Scientific paper
1997-07-23
Physics
Condensed Matter
RevTeX, 7 eps figures included in this revised version
Scientific paper
An experimental study of bifurcations associated with stability of stationary points (SP's) in a parametrically forced magnetic pendulum and a comparison of its results with numerical results are presented. The critical values for which the SP's lose or gain their stability are experimentally measured by varying the two parameters $\Omega$ (the normalized natural frequency) and $A$ (the normalized driving amplitude). It is observed that, when the amplitude $A$ exceeds a critical value, the normal SP with $\theta=0$ ($\theta$ is the angle between the permanent magnet and the magnetic field) becomes unstable either by a period-doubling bifurcation or by a symmetry-breaking pitchfork bifurcation, depending on the values of $\Omega$. However, in contrast with the normal SP the inverted SP with $\theta=\pi$ is observed to become stable as $A$ is increased above a critical value by a pitchfork bifurcation, but it also destabilizes for a higher critical value of $A$ by a period-doubling bifurcation. All of these experimental results agree well with numerical results obtained using the Floquet theory.
Jang J. W.
Kim Sang-Yoon
Shin Sun-Hee
Yi Jiang
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