Attitude dynamics of classical dumbbell problem with solar radiation pressure

This work extends the attitude dynamics and stability properties of the classical planar dumbbell problem, namely, two masses connected by a rigid massless tether [1–3], by considering the effect of a solar radiation pressure (SRP) gradient between the tip masses. In principle, this SRP gradient can be used as a means of attitude station keeping of tethered satellite systems, without the need for mechanical systems or thrusters to maintain a fixed attitude. Attitude stabilization of a satellite by SRP was first proposed in 1959 [4] and was studied
further in 1965 [5], the latter of which considered differential reflectivity on the spacecraft due to local surface irregularities. Since then, the concept of employing differential SRP for semipassive attitude control and stabilization of tethered satellites, for example, using articulated reflective surfaces, was investigated in [6].
This work adapts the widely used model of a tethered satellite system [7,8] by introducing SRP forces to the tip masses, acting in the radial direction from the Sun. Therefore, lightness numbers are assigned to the masses, which is equivalent to assigning a variable surface reflectivity. This can be achieved, for example, using electrochromic coatings that consist of an electroactive material that changes its surface reflectivity according to an applied electric potential [9,10]. When a long tether is orbiting a central body, the relative attitude of the system affects the total force acting on the dumbbell’s center of mass (c.m.). This means that the equations of motion (EOM) describing the orbit and attitude of the system are coupled [11].