In multibody dynamic analysis, one of the most important problems is to reduce computation times for real-time simulation. This paper presents the derivation procedure of equations of motion of a 6${ imes}$6 autonomous vehicle in terms of chassis local coordinates which do not require coordinates transformation matrix to enhance efficiency for real-time dynamic analysis. Also, equations of motion are derived using the VT(velocity transformation) technique and symbolic computation method coded by MATLAB. The Jacobian matrix of the equations of motion of a system is derived from symbolic operations to apply the implicit integration method. The analysis results were compared with ADAMS results to verify the accuracy and approve the feasibility of real time analysis.