Effect of Vibration on the Accuracy of a Vertical Reference Pendulum

Abstract

The pendulum has been used from ancient times as a means of establishing a local vertical reference. One of the earliest accounts of the use of the pendulum as a plumb-bob comes from Thebes, Egypt, about 1,100 B.C. [l, p. 4811. As the years passed, the requirements for accuracy have increased until today the accuracy requirements for missile applications are such that second order effects may determine whether or not the pedulum may be used to establish a local vertical reference. Using the best techniques currently available, it is impossible to eliminate entirely the vibration transmitted through the supporting structure to the point of support of the pendulum. The purpose of this paper is to examine the effect of such residual vibration on the accuracy of a pendulum type vertical reference. It will be shown that if the vertical and horizontal components of acceleration of the point of support of the pendulum are correlated in time, then in general the mean position of the pendulum does not coincide with the local vertical axis. This zero-shift, or Auswanderungs-phenomenon, is not new, having received considerable attention in the German literature of the 1930's, notably by Klotter and his associates [2], [3] and Erdelyi [4]. More recently, problems of this type have been studied by Weidenhammer [5] and Conrad and Shellhorn [6]. Except for [6] the analysis was restricted to weak damping and the case of harmonic excitation, where both vertical and horizontal components of the acceleration of the point of support have the same frequency. In the present study the analysis will be for heavily damped systems acted upon by a class of bounded excitations having zero time average.