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Existing reachability and optimal control theory are applied to a class of nonlinear systems with ellipsoidal initial reachability sets. Analytical expressions for general state partition extrema are developed, yielding necessary conditions for reachability as well as tools for significant reduction in reachability computation. Similar relations for position and velocity reachability set surface computation are also developed and the computation implications discussed. Several examples are worked to illustrate results, and finally directions for future work are discussed.