Abstract The problems of the aerodynamic heating through the turbulent boundary layer of a thin flat plate is discussed in view of the unsteady temperature distribution along the surface.
The fundamental system of equations for a turbulent boundary layer of a compressible fluid consists of the conservation equations for mass, momentum and energy, the equation of state and the equations describing the transport properties of air. The solutions depend upon the boundary conditions on the surface of a plate. For the temperature distribution in the boundary layer, either the adiabatic-wall assumption or the equitemperature-wall condition has usually been postulated, simply for the convenience of analysis. But strictly speaking, the temperature is hardly regarded as uniform.
On the other hand, the wall temperature should be determined by solving the equations of heat conduction in the plate which is under the influence of aerodynamic heating through the boundary layer. However, because the rate of aerodynamic heating depends on the boundary layer flow, the heating rate itself turns out to be dependent on the wall temperature. This means that the boundary layer over a plate and the heat conduction in a plate must be solved simultaneously. Since we are interested in the temperature distribution over the wall, the problem will be reduced to that of determining the surface temperature by introducing the heat transfer rate through the boundary layer with arbitrary temperature distribution in the equation of heat conduction.
Using FERRARI's formula for the aerodynamic heat of the turbulent boundary layer, we obtained numerical results for a thin steel plate of 10 mm thick. The theoretical unsteady temperature distributions are compared with the experimental results.

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Abstract The gravity gradient stabilization provides a passive, long-lived and earth pointing satellite attitude control system. The fundamental principles of the gravity stabilization are showed, and then the equations of motions are derived by applying the Lagrangean equations to the proposed system which is composed of the main rod, damping rods and damper-spring mechanisms. As a result of linearization, these equations are expressed in two groups, one describing the pitch motions and the other the roll-yaw motions. The equations for pitch have two oscillatory transient modes; one is symmetric, and the other antisymmetric, and the characteristics are represented by three non-dimensional parameters related to the moment of inertia, spring constant and damping constant. Orbital eccentricity introduces a driving torque to cause the steady harmonic oscillations in pitch.
There exist a cross-coupling between the roll and yaw motions due to the Coriolis forces, but if these cross terms are neglected and the time base transformation is performed, the roll equations reduce to the pitch equations. Therefore the results for pitch are applicable for roll. The effect of the coupling torque is to provide damping of the yaw motions.
The method for selecting the parameters to yield optimum results is examined and the performance of the system for thus obtained parameters is that the time to half-amplitude is within 0.3 orbit and that the orientation error due to the orbital eccentricity is below 1.8° for the eccentricity of 0.01.

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