the French TGV, at . Kinematic analysis While a qualitative description provides some understanding of the phenomenon, deeper understanding inevitably requires a mathematical analysis of the vehicle dynamics. Even then, the results may be only approximate. A kinematic description deals with the geometry of motion, without reference to the forces causing it, so the analysis begins with a description of the geometry of a wheel set running on a straight track. Since Newton's second law relates forces to the acceleration of bodies, the forces acting may then be derived from the kinematics by calculating the accelerations of the components. However, if these forces change the kinematic description (as they do in this case) then the results may only be approximately correct. Assumptions and non-mathematical description This kinematic description makes a number of simplifying assumptions since it neglects forces. For one, it assumes that the rolling resistance is zero. A wheelset (not attached to a train or truck), is given a push forward on a straight and level track. The wheelset starts coasting and never slows down since there are no forces (except downward forces on the wheelset to make it adhere to the track and not slip). If initially the wheelset is centered on the railroad track then the effective diameters of each wheel are the same and the wheelset rolls down the track in a perfectly straight line forever. But if the wheelset is a little off-center so that the effective diameters (or radii) are different, then the wheelset starts to move in a curve of radius (depending on these wheelset radii, etc.; to be derived later on). The problem is to use kinematic reasoning to find the trajectory of the wheelset, or more precisely, the trajectory of the center of the wheelset projected vertically on the roadbed in the center of the track. This is a trajectory on the plane of the level earth's surface and plotted on an - graphical plot where is the distance along the railroad and is the "tracking error", the deviation of the center of the wheelset from the straight line of the railway running down the center of the track (midway between the two rails). To illustrate that a wheelset trajectory follows a curved path, one may place a nail or screw on a flat table top and give it a push. It will roll in a circular curve because the nail