Second-order theory of the rotation of an artificial satellite

This work presents the expansion of the second-order of an analytical theory of the attitude evolution of an artificial satellite perturbed by given torques. The first-order of the theory has already been presented by the author in Celestial Mechanics39 (1986) 309–327. It is a theory that is valid under very general conditions including slow rotation and inequal axes of inertia. The present theory is suitable for any internal or external disturbing forces producing the torques. A formal solution is expanded in the second-order according to powers of a small parameter characteristic of the order of magnitude of the disturbing torques. These torques are expanded in Fourier series and the theory applies whatever is the length of these series. The coefficients of the solution are given by an iterative formation law. The comparison of the results with a numerical integration based upon a HIPPARCOS model shows that the second order has brought an improvement to the theory by at least one order of magnitude over the results of the first order.