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We present an outline of a technique to associate certain methods from timeoptimal quantum control with various transforms on SU(3). Unitary operators aretaken from certain time dependent Hamiltonians and transformation laws arederived. A methodological framework for development of solution for these typesof problems with a non-simple geometric framework is presented that isgenerally applicable. We give an expansive overview of the field of SU(3), itsmeaning, purpose and context within the presented results. Exact solutions forperiodic curves on SU(3) are provided, along with the operators and physicalframework that surrounds them. A comprehensive review of the literature andestablished results is given for reference. Discussion is given in full toeffective approaches that may be given both to the teaching of the subject, andthe development of further results within the science. We conclude the paperwith an overview of new avenues of investigation that are opened through theresults that are presented.

Time Evolution Operators for Periodic SU(3)