Approximate expressions of mean eddy current torque acted on space debris

Abstract

Rotational state of space debris will be influenced by eddy current torque which is produced by the conducting body rotating within the geomagnetic field. Former expressions of instantaneous torque established in body-fixed coordinate system will change in space during rotation due to the variation of the coordinate system. In order to further investigate the evolution of the rotation of space debris subjected to the eddy current torque, approximate expressions of mean eddy current torque in inertial coordinate system are obtained from the average of the Euler dynamics equations under the assumption that two of the principal moments of inertia of the space debris are similar. Then the expressions are verified through numerical simulation, in which the orientation of the averaged variation of angular momentum is in agreement with the torque from the expressions, which is on an identical plane with magnetic field and the angular momentum. The torque and the averaged variation of the angular momentum have the same evolution trend during rotation in spite of minor deviations of their values.