Ok, so here is my question In grade school we all learned that the shortest distance between two points is a straight line. We also know from intuition that cars can't withstand infinite amounts of radial or tangential acceleration otherwise the car will skid i.e traction circle. Via this intuition experienced drivers in an auto racing situation in an effort to reduce the time it takes to go around a race circuit the driver will take a "racing line". Which most people simply "see" and do not calculate. My end goal is to figure out what the racing line or path of a (or any) given race course is and corresponding velocities subject to the maximum allowed forces from the traction circle. From what I have read I think the most general way to solve something like this with out discreetly computing paths is to use variational analysis; but I really don't understand it. Is there a less technical resource on the subject? Or an alternative solution? also is there be a way of doing this via viewing the course as a field of curvature and then finding the gradient of the curvature path?