Brachistochrone problem solved by invariant imbedding, dynamic programming, and quasilinearization methods

In such fields of current interest as optimal control and orbit determination, non-linear two-point boundary-value problems arise, the numerical solutions for which are difficult to obtain. In this thesis, some of the useful tools for treating problems of this nature - invariant imbedding, dynamic programming, and quasilinearization are studied by means of the brachistochrone problem. The three approaches are used separately and in combination. Computer programs using MAD language are presented. The results are compared with the classical solutions.