The twin rotor damper (TRD) is a device which primarily utilizes centrifugal forces for active vibration control. In its basic form, the TRD consists of two eccentric control masses rotating about two parallel axes. In a preferred mode of operation, the continuous rotation mode (CRM), the control masses rotate in opposite directions with a constant and equal angular velocity. This rotational motion results in a harmonic control force. In previous research, it has been shown that, in the CRM, the TRD can effectively damp vibrations while requiring little to no power from its actuators. However, this holds only for lateral vibrations, vibration perpendicular to gravitational forces, ergo gravity has no influence on the motion of the control masses. In this paper, the influence of gravity on the CRM is investigated analytically for the first time. It is shown that the TRD requires substantially greater power in the CRM to periodically lift the control masses against gravity. Subsequently, the CRM is augmented with an auxiliary function in the form of a Fourier series. This function is optimized such that the increase in power due to gravity is minimized while maintaining the damping performance of the TRD. The effects of augmenting the CRM are investigated, and a control algorithm is developed for the operation in the augmented CRM. In a numerical design example, it is shown that, with the augmented CRM, the power efficiency of the TRD can be regained at the cost of moderately reducing its damping performance.