Time optimal rest-to-rest reorientation of a rigid spacecraft with an arbitrary initial attitude and distinct principal moments of inertia is discussed. The effect of the gyroscopic coupling terms in Euler's equations on the control switch times is shown. A method for recursively generating coefficients for a truncated Taylor series solution of Euler's equations and the differential equations for the Euler parameter state transition matrix is shown. These solutions are used to solve for the optimal control switch times.
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