Papers Published

1. Wilson, James F., Parametric spin resonance for a spinner with an orbiting pivot, International Journal of Non-Linear Mechanics, vol. 33 no. 2 (1998), pp. 189 - 200 [S0020-7462(97)00020-6] .
   (last updated on 2007/04/09)

   Abstract:
   Dynamics are investigated for a rigid spinner with a hole, concentric with its mass center, into which a pivot is loosely fitted. As the spinner is excited by the motion of the contacting pivot, the spinner may sustain a quasi-steady spin angular velocity θ in the pivot's orbiting plane. This spin motion, defined as parametric spin resonance (PSR), is investigated for the case of prescribed, bi-directional, harmonic pivot motion of frequency ω. The ranges of the system's non-dimensional parameters needed to achieve PSR are determined. Experimental data both explain the spinner's direction of rotation and complement the predicted existence of quasi-steady values of θ. The analysis explains the characteristic motions of such toys as the Hula-Hoop and the Indian Windmill (the Gee-Haw Whimmy Diddle), and in general may explain certain unwanted vibrations in machinery with worn or loosely-fitting bearings. © 1997 Elsevier Science Ltd.