The mean square stability of an inverted pendulum subject to random parametric excitation

✍ Scribed by M.S. Howe

• Publisher: Elsevier Science
• Year: 1974
• Tongue: English
• Weight: 859 KB
• Volume: 32
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1016/s0022-460x(74)80096-9

✦ Synopsis

This paper describes a theory of the stabilization of an inverted pendulum by means of externally imposed random oscillations of the point of support in a vertical line. Methods previously used in the multiple scattering theory of wave propagation in random media are applied to derive two conditions for stability in the upright position. The first of these is the well-known condition which requires the variance of the support velocity to be large. The second condition has apparently not been explicitly noted hitherto, and relates to the parametric amplification of the pendulum oscillations caused by resonant hlteractions between the steady pendulum motion at frequency k, say, and those spectral components of the effective excitation at precisely twice that frequency. The theor,) is compared with recent results of analogue computer simulations and found to be in good qualitative agreement.