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The selection of an appropriate method for modeling vehicle dynamics heavily depends on the application. Due to the absence of human intervention, the demand for an accurate and real-time model of vehicle dynamics for intelligent control increases for autonomous vehicles. This paper develops a multibody vehicle model for longitudinal-vertical dynamics applicable to advanced driver assistance (ADAS) applications. The dynamic properties of the chassis, suspension, and tires are considered and modeled, which results in accurate vehicle dynamics and states. Unlike the vehicle dynamics models built into commercial software packages, such as ADAMS and CarSim, the proposed nonlinear dynamics model poses the equations of motion using a subset of relative coordinates. Therefore, the real-time simulation is conducted to improve riding performance and transportation safety. First, a vehicle system is modeled using a semi-recursive multibody dynamics formulation, and the vehicle kinematics and dynamics are accurately calculated using the system tree-topology. Second, a fork-arm removal technique based on the rod-removal technique is proposed to reduce the number of bodies, relative coordinates, and equations constrained by loop-closure. This increase the computational efficiency even further. Third, the dynamic simulations of the vehicle are performed on bumpy and sloping roads. The accuracy and efficiency of the numerical results are compared to the reference data. The comparative results demonstrate that the proposed vehicle model is effective. This efficient model can be utilized for the intelligent control of vehicle ADAS applications, such as forward collision avoidance, adaptive cruise control, and platooning. Full article