Tables of the Theodorsen Circulation Function for Generalized Motion

Important in all stability, aeroelastic, and flutter problems is the Theodorsen C(k) function. Tables of this function are well known if the motion is harmonic. Heretofore, tables of the Theodorsen function for generalized motion have not been available. In this report, the latter tables are given for a range that should be sufficient to meet the needs of aerodynamicists. W. P. Jones has given a discussion of the generalized Theodorsen function, but his results appear incorrect, for, in his analysis, the Theodorsen function as derived by approaching harmonic motion from the side of stability and from the side of instability is distinct. If the Jones analysis were true, the nonuniqueness of the Theodorsen function would imply that the Bessel functions are not continuous, which is indeed false. The difficulty is clarified in this paper.