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The purpose of this paper is to develop analytic solutions for a tethered satellite system (TSS) subjected to internal tether tension moment and external aerodynamic torque for spin-up and spin-down manoeuvres.

Analytic solutions for TSS based on the approximation of Euler’s equations of motion via Fresnel integrals and sine and cosine integrals. Test simulation was performed for two cases (spin-up and spin-down manoeuvres). The conclusion is based on graphical interpretation.

The effects of angular velocities on X, Y and Z axes of the TSS under the influence of combined torques from internal tether tension and external aerodynamic drag influenced during spinning manoeuvres are shown graphically.

This research focuses only on a circular orbit, which is one of the simplest orbits without many variables taken into account such as flight path angle and true anomaly. It could get quite complex for other orbit types like elliptic and parabolic orbits.

Practical implications include observing the stability rotational motion of TSS so as to perform a two-way payload exchange via momentum transfer.

In this paper, analytic solutions for a torque motion of a TSS comprising non-linear Euler’s equations of motion are established for spin-up and spin-down manoeuvres.