On the dynamics of a parametrically excited planar tether

This study is concerned with a planar tether containing payloads in which two lumped masses are fitted whose mutual distance can be contrived to change periodically in time. This periodical variation in distance of the two masses is symmetrical and results in a time-varying coefficient of the kinetic energy, which in turn introduces parametric excitation into the equation of motion. It is assumed that the centre of mass of the symmetrical tether system moves along a circular orbit. First, the case when the orbital angular velocity is constant is examined, and it is shown numerically that three qualitatively different motions can occur. The charts produced can be used to choose parameters for the parametric excitation that yield a desired motion of the tether, such as, for example, spinning, or libration. Then, the case of a zero-valued orbital angular velocity and small oscillations is examined analytically to show how parametric excitation influences the stability of a trivial equilibrium position.