The Moon's Physical Libration in Longitude and Mathieu's Equation

Abstract

A new expansion of the Moon's physical libration in longitude is given. The result has been obtained by replacing integration of a simple second order differential equation with contant factor by a solution of the corresponding differential equation of Mathieu's type. The coefficients of the expansion obtained for the longitude as a function of the time are given in algebraic form and the existence of new singular points of the expansion is signalized.