In general, understanding dynamics is important in control of mechanical systems including robotic systems. In this talk, I will talk about a remarkable dynamic memory effect of viscous damping friction on the motion of underactuated mechanical systems, which is named the damping-induced self-recovery phenomenon. If an underactuated mechanical system without any energy storing elements but with Abelian symmetry under influence of damping friction gets deviated initially from rest by a control force that disappears in the end, then the system asymptotically recovers its way back to its starting state as if it remembers its initial configuration. Damping-induced self-recovery turns out to be a general phenomenon that occurs over a wide range of magnitude of damping or viscosity, including the momentum conservation principle as an extreme case of damping-induced self-recovery with zero damping in which case recovery takes an infinite amount of time, i.e., never takes place, and the kinematic reversibility of low-Reynolds number fluid flows as the other extreme case of damping-induced self-recovery with infinitely large viscosity in which case recovery is instantaneous. I will present both theory and experiments on this remarkable phenomenon.