ИСТИНА

Originally we deal with different simplifications of a well-kmown Goddard problem on a maximization of a result altitude of rocket flight. We have considered a number of possible simplifications of the original problem to find the simplest variant in which, however, the optimal trajectory is obtained in a non-trivial form and still may contains a singular arc. For such a problem we obtain a numerical algorithm to find the following: "treshold value" of a final time such that for all greater final times the optimal trajectory contains singular arc while for all smaller final times the optimal control is of bang-bang form. the start and the end times of a singular subarc in the case of bang-singular optimal control For the computations and visualization we use C# / F# class libary for the numerical solution of ODE systems developed in collaboration with Microsoft Research, Cambridge specialists.