The research described in this paper aimed to study the cornering resistance and dissipation power on the tire contact patch, and to develop an efficient direct yaw moment control (DYC) during acceleration and deceleration while turning. A previously reported method , which formulates the cornering resistance in steady-state cornering, was extended to so-called quasi steady-state cornering that includes acceleration and deceleration while turning. Simulations revealed that the direct yaw moment reduces the dissipation power due to the load shift between the front and rear wheels. In addition, the optimum direct yaw moment cancels out the understeer augmented by acceleration. In contrast, anti-direct yaw moment optimizes the dissipation power during decelerating to maximize kinetic energy recovery. The optimization method proved that the optimum direct yaw moment can be achieved by equalizing the slip vectors of all the wheels. This research also found that this control method enhances the stability of vehicle motion.