Inertial Motion Viewed from a Potential Well

Abstract

he motion of a mass undergoing free horizontal motion on a planet?s surface is analyzed in an inertial frame by using a potential well presentation. The following results from the conventional analysis in rotating coordinates are also found in inertial coordinates. Under typical circumstances the mass oscillates about the latitude where its angular momentum per unit mass matches that of the planet?s surface. For masses with nonzero angular momentum, conservation of angular momentum bounds the mass away from the pole. Motion with zero angular momentum is confined to a fixed meridian plane on which the mass may oscillate across the pole. Motion across the equator is possible only for masses with sufficient energy. Masses with angular momentum per unit mass greater than that of the planet at the equator oscillate about the equator with a limiting period determined by the excess angular momentum.