On the behavior of a heavy body in motion relative to the surface of the earth

The present paper studies the behavior of a point object with mass sliding without friction on the polished circumference of a sphere which turns around a vertical diameter; the influence of the rotation of the earth is treated according to the theory of vibrations about a stationary state. The traditionally accepted simplifying assumptions are examined, and the vectoral method is used to derive the equation of motion. In order to analyze the influence of the rotation of the earth in this problem of nonlinear mechanics, the theory of weak periodic perturbing forces is employed. The theoretical results obtained form the basis for a proposed experiment which would take place in a vacuum with the aid of rod systems or vibrating crystals and involve rotation around a vertical axis.