The flapping motion of hingeless blade which has the preconing angle is analyzed by considering flapping feathering. coupling with generalized normal mode method. The rotor blade is assumed to be infinitely stiff in torsional and chordwise bending, and has the flapwise flexibility with nonuniform mass and stiffness distributions. It is shown that the thrust equation can be represented in terms of the normal mode shapes and the associated natural frequencies like the hub moment. For this representation of the thrust and hub moment, it is also shown that the desirable number of blade is more than four in the vibration problem, and that thrust and hub moment must be represented by the first three and two normal modes of flapwise bending respectively. On the other hand, the expressions of the thrust and hub moment which are represented in terms of the aerodynamic and inertia loadings, are fairly accurate by the first bending mode shape only. The theoretical calculations of the stability and control derivatives by this analysis coincide fairly with the step by step integration method, and with the results of the wind tunnel test for the dynamic model rotor.
The spin decay of our first scientific satellite "Shinsei" (1971-080 A) seems to give a clear evidence to the statement that a spin-stabilized earth satellite suffers the spin decay resulting from energy losses in the form of eddy currents and/or magnetic hysteresis. The analysis of the spin decay is presented in this paper, together with the observed data. A close corelation is found between the rate of spin decay and the magnitude of geomagnetic field component normal to the spin axis. With the aid of the torque measurement using a torque-meter, it is concluded that the torque due to the magnetic hysteresis is negligibly small as compared to the one due to the eddy currents. The average torque acting on Shinsei in its orbit is estimated to be roughly 12 dyne-cm.