An application of the dynamics of a particle in a predetermined path: the problem of the ellipsoidal igloo

Abstract In the present work the classical problem of a particle which describes a segment of a circular path while sliding over a polished spherical surface of an igloo is extended to the case of an ellipsoidal igloo. In this case, the height in which the particle loses the contact with the surface of the igloo obeys a cubic equation whose coefficients depends on the parameters that determine the elliptical path. The analytical solution of this equation is then obtained through the method of Cardano-Tartaglia.