The dynamics analysis of a special rotating differential which situating to the variable tread vehicle steering function is carried out. Firstly,treating this differential gear transmission system as spring-mass of the nonlinear time-varying system with coulomb damping,a bend-torsion coupled vibration model with 12 DOFs is established. Then,considering the road to the wheel load torque in the process of the corners to be external incentive conditions of system,the affect of internal incentive factors on vibration characteristics of this differential gear transmission system is analyzed and the dynamics mathematical model is built. At last,by calculating this mathematical model and natural frequency,the phase path analysis is carried out and the characteristic parameters of this gear transmission system are optimized. The purpose of weakening the oscillation of the system performance and improving the response speed of system,making the system with satisfactory dynamic performance indicators are achieved.