Wiggling the End of a Tether

This is a stub - more explanation later.

Free tethers hanging vertically in zero gee will have transverse ripples, string vibration waves, moving up and down the tether at the transverse propagation speed \sqrt{ T / m } where T the tension in Newtons and \rho is the mass density in kilograms per meter. ( Note that I am using m rather than the usual \mu , because \mu is used for the gravitational parameter ).

Removing the transverse ripples at the ends will be difficult. In the electrical transmission line analogy, the end mass acts like a capacitor, adding resonances but not removing vibrational energy. The only way to remove energy is with transverse movements, and there is nothing to push transversely against (except perhaps rocket engines).

Long wavelength transverse waves are not the biggest problem, since most practical difficulties arise from curvature, which is the inverse square of wavelength. This page focuses on removing the short wavelength perturbations. "Removing" means dissipating the energy - something must store or dissipate energy for the vibrations to dampen.

An end mass that is a hanging rigid beam with three or four large momentum wheels may be one way to do this. The momentum wheels are on electric motors, torquing against the beam, with rotational energy transferred from wheel to wheel. That will make the end of the beam move transversely. While the system will likely need some power from solar cell arrays, it may derive much of its power from the vibrations themselves.

MORE LATER