On the precession of the elliptic mode shape of a circular ring owing to nonlinear effects

Abstract

The Foucault pendulum, which maintains the plane of its vibrations in inertial space, loses this property as soon as the trajectory ceases to be flat. If the pendulum end circumscribes an elliptic trajectory instead of a straight line segment, then this ellipse precesses in the same direction as the material point circumscribes the ellipse itself. In this case, the angular velocity of the ellipse precession is proportional to its area and can be explained by the nonlinearity of the equations of vibrations of a mathematical pendulum [1].