Dynamics of spin-stabilized satellites during extension of long flexible booms

Nomenclature b = perpendicular distance of boom root from ig E2(£), E9(£) = nondimensional mode shapes for boom vibration in J2, ja directions, respectively El = flexural stiff ness of boom h = perpendicular distance of boom root above ii, iz plane ii,i2,ia = principal axes of main body, i3 is nominal spin axis ji, J2,J3 = boom base set of axes, ji is nominal boom line I = inertia tensor of main body /n,/22,/33 = principal moments of inertia of main body along iii 12, is, respectively l(t) = length of boom Mb,Mt = boom and tip total masses Mm = mass of main body M8t — total satellite mass s = distance along boom center line from boom root to point on boom x = position of mass element of boom as seen in ji, J2, js set a3,a2,ai = Euler angles (3,2,1 sequence) relating ii, i*, is to inertial attitude axes at main body mass center. Axis 3 of both sets parallel in nominal spin azD = change in spin rate = modal amplifiers i.e., x2 = $2%, %s = &*lEz = angle between ji and ii measured on projection of ji in ii — i2 plane = mass per unit length of boom = angular velocity of main body -main body center of mass