1. The use of a principal axis system as a reference for the equations of motion has been a standard i n vibration and flutter analysis of unrestrained vehicles for many years. In 1962 a comprehensive statement of the various structural dynamics problems of the unrestrained vehicle was given by Bisplinghoff and Ashley' using a centroidal principal axis system. The use of attached, mean, and principal axes was discussed by Milne i n 19642 and the distinction between mean and principal axes was further clarified i n 19683. The mean and principal axes are the same when transverse displacement i s the primary degree of freedom, i.e., when rotatory inertia effects can be neglected (as we assume i n the present development). The use of a principal axis system i n flight mechanics was further refined i n the FLEXSTAB computer program developed by Dusto and his associates at the Boeing Co. from 19684 t o 19745. The conclusion from these investigations i s that principal axes, rather than attached axes, must be used i n the equations of mot ion.
2. 7-9 have one assumption i n common: that the solution t o the equations of motion w i l l be invariant with the choice of support system used t o determine the SIC's if this support system i s unloaded i n the unrestrained f l i g h t condition. This i s a necessary and sufficient condition for a trimmed loads solution only, and the loads solution of Rowan and Burns 10 i s therefore correct. However, it i s not sufficient for the maneuvering solution. The conditions for a correct maneuvering solution require not only an unloaded support system but also, and obviously, that the moments equal the rate of change of angular momenta. These conditions w i l l be realized i f the principal axis formulation of the equations of motion i s employed. However, an a1ternate formulation that retains the convenience of an arbitrary attached axis system can s t i l l be used i f the location of the principal axes i s duly noted i n the formulation. This alternate formulation i s the subject of the present paper.
3. For the analysis of the aeroelastic characteristics of a restrained vehicle, the vehicle f l e x i b i l i t y can be represented by a matrix of SIC's which permit the calculation of the structural deflections relative t o a statically determinate support system (the SIC constraint point(s)) located conveniently within the vehicle (e.g., near the intersection of primary wing and fuselage structural components). The aeroelastic analysis must consider not only the aerodynamic forces that arise from vehicle incidence and control surface rotations, but also the aerodynamic forces that arise from the deflections (considered as i n i t i a l deflections such as camber and twist) caused by the inertial forces that would exist i n free flight. This approach leads t o a series of inertial aeroelastic coefficients corresponding t o unit accelerations i n addition t o the more conventional aeroelastic coefficients. An example of this approach i s given i n Sect. 8-3 of Ref. 11, i n which the effect of normal load factor on a wing i s considered.