Subharmonic resonances of the parametrically driven pendulum
نویسنده
چکیده
A simple qualitative physical explanation is suggested for the phenomenon of subharmonic resonances of a rigid planar pendulum whose axis is forced to oscillate with a high frequency in the vertical direction. An approximate quantitative theory based on the suggested approach is developed. The spectral composition of the subharmonic resonances is investigated quantitatively, and the boundaries of these modes in the parameter space are determined. New related modes of regular behaviour are described and explained. The conditions of the inverted pendulum stability are determined with a greater precision than they have been known earlier. A computer program simulating the physical system supports the analytical investigation. PACS numbers: 5.45.-a, 05.10.-a, 07.05.Tp, 45.10.-b
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تاریخ انتشار 2002