1. Amodal analysis of a free spacecraft idealized as a system with 6n degrees of freedom yields 6n-6 natural modes of deformation and six rigid body modes. Let 771, 772, ^en-e represent the deformation modes, and ?76n_5, rj&nthe rigid body modes. In vibration analysis, all y* are composed of all rji in general [see (27)], and both sets of variables are assumed small. In the present problem, the reference frame B has been so defined as to accommodate the contributions of the rigid body modes, and the variables uirare comprised of only the deformation mode contributions. Thus the constraint equations defining B are used in writing the transformation