Systems and methods for damping torsional oscillations of downhole systems are described. The systems include a damping system configured on the downhole system. The damping system includes a first element and a second element in frictional contact with the first element. The second element moves relative to the first element with a velocity that is a sum of a periodic velocity fluctuation having an amplitude and a mean velocity, wherein the mean velocity is lower than the amplitude of the periodic velocity fluctuation.