This paper is based on the kinematic and dynamic analysis of smooth driving of a vehicle in a curve. The lateral movement of the vehicle is necessary to follow the bends of the roads and to choose one's own route at intersections, as well as to avoid obstacles that appear laterally. Lateral dynamics involves motion analysis in the vehicle coordinate system that introduces curvilinear motion as the coordinate system rotates as the vehicle turns. We connected the vehicle and wheel coordinate systems via Ackermann geometry and parallel geometry, and we reduced the vehicle to a single-track model for easier calculation and understanding, but retaining all the most important phenomena. We carried out simulations and calculations of vehicle turning in a curve in the Modelica program and thus gained an insight into the dynamics and behavior of the vehicle when turning. We analyzed the vehicle in a stable state of turning, which means that all the time derivatives of the vehicle's speed are equal to zero. The physical understanding is then that the vehicle drives in a circle with a constant turning speed. Then we analyzed the vehicle's controllability under various driving conditions (under-, neutral and over-) and movement (acceleration, deceleration). At the very end, we presented a couple of functions that are used for lateral control of vehicles such as ESC.LKA and others