In the adaptive scheme presented by Slotine and Benedetto [1] for atti
tude tracking control of rigid spacecraft, the spacecraft is parameter
ized in terms of the inertial frame. This note shows how a parameteriz
ation in body coordinates considerably simplifies the representation o
f the adaptation scheme. The new symbolic expression for the regressor
matrix is easy to find even for 6 degrees of freedom (DOF) Hamiltonia
n systems with a large number of unknown parameters. If the symbolic e
xpression for the regressor matrix is known in advance, the computatio
nal complexity is approximately equal for both representations. In the
scheme presented by Slotine and Benedetto [1] this is not trivial bec
ause the transformation matrix between the inertial frame and the body
coordinates is included in the expression for the regressor matrix. H
ence, implementation for higher DOF systems is strongly complicated. A
n example illustrates the advantage of the new representation when mod
eling a simple 3 DOF model of the lateral motion of a space shuttle.