Dumbbell librations in elliptic orbits

Abstract

This paper discusses and analyzes the first-order effect of oibital eccentricity on the planar tumbling or oscillatory motion of a dumbbell-shaped satellite This has been done by assuming that the angular orientation angle S^ can be represented by a power series in eccentricity e, in which the coefficient of the e° term was set equal to the circular solution S£ available from earlier investigations The differential equation for the coefficient of the e term is shown to be of an inhomogeneous Mathieu type, the particular solutions of which can be readily obtained if certain weak restrictions are placed on the initial magnitude of the dumbbell's angular velocity The analysis indicated that the orientation of the satellite in the elliptic orbit can differ substantially from the one determined for the circular orbit