  The basic module for the solution of the minimum time optimal control of a
car-like vehicle is herein presented. The vehicle is subject to the effect of
laminar (linear) and aerodynamic (quadratic) drag, taking into account the
asymmetric bounded longitudinal accelerations. This module is studied and
designed to be fast and robust in sight to be the fundamental building block of
a more extended optimal control problem that considers a given clothoid as the
trajectory and the presence of a constraint on the lateral acceleration of the
vehicle. The nonlinear dynamics and the different possible boundary conditions
yield different analytical solutions of the differential equations, hence they
by themselves a particular attention. The study of the numeric stability of the
computation for limit values of the parameters is essential as showed in the
numerical tests.
