Bifurcations in a parametrically forced magnetic pendulum

초록

An experimental study of bifurcations associated with the 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 [Formula Presented] (the normalized natural frequency) and [Formula Presented] (the normalized driving amplitude). It is observed that, when the amplitude [Formula Presented] exceeds a critical value, the normal SP with [Formula Presented] ([Formula Presented] 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 [Formula Presented]. However, in contrast with the normal SP the inverted SP, with [Formula Presented] is observed to become stable as [Formula Presented] is increased above a critical value by a pitchfork bifurcation, but it also destabilizes for a higher critical value of [Formula Presented] by a period-doubling bifurcation. All of these experimental results agree well with numerical results obtained using the Floquet theory. © 1997 The American Physical Society.