Study on the eddy current damping of the spin dynamics of space debris from the Ariane launcher upper stages

This paper addresses the topic of damping of the spin dynamics of a spatial debris orbiting around the Earth. Such debris, which can consist of parts of heavy launchers such as the Ariane rocket under consideration in this article, are impacted by torques generated by eddy currents as their conducting non-ferromagnetic body orbits through the Earth magnetosphere. Several previous works have focused on describing this induction phenomenon and have proposed analysis of empirical observations of this particular and important effect which has attracted much attention since the number of spatial debris has emerged as a problem for the future of space programs, especially in low orbits. In this paper, we present a relatively comprehensive modeling of the induction phenomenon, by means of Maxwell's equations inside the conducting and non-ferromagnetic body. Through the generalized Ohm's law, we show how one can obtain a partial differential equation with Neumann's boundary conditions problem that, once solved, e.g. through a finite elements method, yields the values of induced currents and braking torques. The case of a depleted upper stage of a heavy launcher, having a cylindrical shape and thin walls is particularly studied. We show a methodology to estimate the decay-rate of the spinning velocity, which is proven to satisfy a first-order asymptotically stable linear dynamics. Special cases consisting of typical orbit of space debris are treated.