Summary: [For the entire collection see Zbl 0707.00023.]
The purpose of this paper is to investigate the attitude dynamics of a spinning tethered system in LEO (Low Earth Orbit): a manned module and a counter-weight connected by a tether spin around an axis perpendicular to the tether in order to provide the artificial gravity level required by human physiology during prolonged space travel. The focus of this paper is twofold. First, we analyze the attitude dynamics of the whole tethered system by using an analytical approach in order to show the stability properties of the system considered as an extensible dumbbell. Secondly, we concentrate on the attitude dynamics of one of the end masses, acted upon by a restoring torque provided by the tethered linkage. In the analysis, use has been made of the concept of a rigid body with time- varying principal moments of inertia applied to a body of almost cylindrical shape.
The stability analysis yields to a Mathieu’s equation for the attitude motion of the whole tethered system perturbed from the nominal spin condition and several results from computer simulations are presented in order to show the attitude trend of one end body during the spin-up, stationkeeping and spin-down phases of the motion. We conclude that a growth in the out-of-plane wobbling because of the tether stretching is to be expected whenever appropriate conditions on the moments of inertia ratios are satisfied but the entity of such a motion is too small to represent a real problem and also that some means for controlling the angular motion at least around the longitudinal axis of the tethered system is required if the end bodies approach a cylindrical shape. Results from the simulations agree with the experimental results obtained in the Gemini program.