论文信息 - A pendulum theorem - 字舞流文

A pendulum theorem

We consider N linked pendulums which are inverted and balanced on top of one another, and establish a general theorem which shows how they may be stabilized by small vertical oscillations of the support.

D. J. Acheson | D. Acheson | David Acheson

[1] C. Hsu,et al. ON A RESTRICTED CLASS OF COUPLED HILL'S EQUATIONS AND SOME APPLICATIONS , 1961 .

[2] T. Mullin,et al. Upside-down pendulums , 1993, Nature.

[3] E. R. Lowenstern. XXXIX. The stabilizing effect of imposed oscillations of high frequency on a dynamical system , 1932 .

[4] A. Stephenson. XX. On induced stability , 1908 .

[5] H. Risken,et al. Stability of parametrically excited dissipative systems , 1988 .

[6] D. Jordan,et al. Nonlinear ordinary differential equations (2nd ed.) , 1987 .

[7] H. Kalmus,et al. The Inverted Pendulum , 1970 .

[8] S. Otterbein. Stabilisierung des n-Pendels und der Indische Seiltrick , 1982 .

[9] Sigalia Dostrovsky,et al. The Evolution of Dynamics: Vibration Theory from 1687 to 1742 , 1981 .