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The minimum time attitude slewing motion of a rigid spacecraft with its controls provided by bounded torques and forces is considered. Instead of the slewing time, an integral of a quadratic function of the controls is used as the cost function. This enables us to deal with the singular and nonsingular problems in a unified way. The minimum time is determined by sequentially shortening the slewing time. The two-point boundary-value problem is derived by applying Pontryagin's maximum prinicple to the system and solved by using a quasilinearization algorithm. A set of methods based on the Euler's principal axis rotation is developed to estimate the unknown initial costates and the minimum slewing time as well as to generate the nominal solutions for starting this algorithm. It is shown that one of the four initial costates associated with the quaternions can be arbitrarily selected without affecting the optimal controls and thus simplifying the computation. Several numerical tests are presented to show the applications of these methods.

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