A damping system for damping rotary movements of a tailing arm. The system includes a chassis, a main shaft, and a rotary damping mechanism. The rotary damping mechanism includes a first externally-threaded gear attached fixedly to the main shaft, a guide rail attached fixedly to the chassis, a linear shock absorber, an internally-threaded gear associated with the first externally-threaded gear, and a first actuator configured to decouple the first externally-threaded gear from the linear shock absorber and couple the first externally-threaded gear with the linear shock absorber.