A Continuum Approach to Minimum Time

A continuum approach to the minimum time problem is taken in order to approximately determine the isochrone distribution in the phase plane diagram of a double integrator problem. The approach allows the state variables to be treated as independent variables and time is eliminated from the analysis. The choice of independent variables provides levels of complexity which are the same for both linear and nonlinear systems. For the double integrator problem, continuum relations are derived and an approximate solution is obtained using the finite element method. Plots of the approximate isochrone distribution are provided.