For a three degree-of-freedom（3-DOF）model with discrete natural frequencies，a modified matrix perturbation method is proposed to derive an approximate analytical solution of the real parts of the eigenvalues，which considers both the inertial coupling and aerodynamic stiffness simultaneously. The modified solution shows that the system stability is related to multiple aerodynamic coefficients as the inertial coupling is taken into account. Although the inertial coupling increases the complexity of the stability criterion，a simplified practical expression can be realized in some common scenarios. Taking a D-shape 6-bundled iced conductor as an example，the accuracy of the approximate solution is verified against the numerical solution. The analysis of the modified solution indicates that the additional mass of the system mainly alters the real part of the eigenvalue through the effect of gravity stiffness and inertial coupling，and in turn influences the galloping stability. Meanwhile，these two effects are both coupled with aerodynamic coefficients. The double pendulum commonly used in transmission lines is analyzed based on the modified solution.The results show that the double pendulum can control the galloping effectively under some given wind attack angles. However，if the wind attack angle and aerodynamic parameters get changed，the anti-galloping effectiveness may disappear. The modified solution provides a method to analyze the anti-galloping mechanism of the additional mass on galloping stability，which offers significant guidance for the anti-galloping design of transmission lines