In the adaptive scheme presented by Slotine and Benedetto [1] for attitude tracking control of rigid spacecraft, the spacecraft is parameterized in terms of the inertial frame. This note shows how a parameterization in body coordinates considerably simplifies the representation of the adaptation scheme. The new symbolic expression for the regressor matrix is easy to find even for 6 degrees of freedom (DOF) Hamiltonian systems with a large number of unknown parameters. If the symbolic expression for the regressor matrix is known in advance, the computational complexity is approximately equal for both representations. In the scheme presented by Slotine and Benedetto [1] this is not trivial because the transformation matrix between the inertial frame and the body coordinates is included in the expression for the regressor matrix. Hence, implementation for higher DOF systems is strongly complicated. An example illustrates the advantage of the new representation when modeling a simple 3 DOF model of the lateral motion of a space shuttle.
