Under steady conditions, simplified control equations of atmospheric motion are used to analyze the basic characteristics of cyclones and anticyclones. On this basis, analytic solutions of cyclonic and anti-cyclonic trajectories are derived by qualitatively analyzing and solving ordinary differential equations. By combining the basic characteristics of cyclones and anticyclones, it is demonstrated that positive and negative damping behaviors are present in cyclonic and anti-cyclonic motions and that the physical mechanism of the negative damping in these motions results from various types of horizontal convergence at low levels.