Muster, Douglas F.2022-10-062022-10-06196613846628https://hdl.handle.net/10657/12166In 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.application/pdfenThis item is protected by copyright but is made available here under a claim of fair use (17 U.S.C. Section 107) for non-profit research and educational purposes. Users of this work assume the responsibility for determining copyright status prior to reusing, publishing, or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires express permission of the copyright holder.Brachistochrone.Invariant imbedding.Dynamic programming.Quasilinearization.Thesisreformatted digital