Experimental Study of Inverted Regulable Pendulum Stability

The study identifies stability zones of single, double and triple physical pendulums, regulable in the inverted vertical position by monoharmonic fluctuations of the vertical suspension axis (linear problem). The pendulum links (absolutely solid body) are arranged subsequently and connected by ideal (frictionless) cylindrical joints with parallel axes. The calculated results for the stability zone boundary lines were found be solving the stability problem, this approach being proposed by the authors. The experimental results were obtained by means of original testing facilities specially created for this purpose. The facilities possess the characteristics necessary for solving the two experimental tasks (frequency testing tasks and the problems of defining the stability zone boundaries). We defined stability zone experimental boundaries for a wide range of change of amplitude and frequency excitation parameters. By experiments we confirmed the theoretical prediction of dynamical instability of inverted pendulum systems when crossing the upper boundary of the stability zone. We obtained the experimental results in the area connecting the upper and lower boundary lines of the stability zone. The results obtained in this work, were preceded by a thorough analysis of the experimental material performed by D.J. Acheson and T. Mullin for single, double and triple pendulums.

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