Note that line becomes better than line for wide courses. This is because the speed differential between lines and is very great for wide courses. So, the answer is, under the assumptions made, that the inside line is never better than the classic racing line. For the splice-type car behavior assumed, I conjecture that no line is faster than line . We have gone through a simplified kind of variational analysis .
Variational analysis is used in all branches of physics, especially mechanics and optics.
It is possible, in fact, to express all theories of physics, even the most arcane, in variational form, and many physicists find this form very appealing. It is also possible to use variational analysis to write a computer program that finds an approximately perfect line through a complete, realistic course.