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The problem of a spinning satellite with a partially filled viscous ring damper is investigated. It is shown that there are two distinct modes of motion, the nutation-synchronous mode and spin-synchronous mode. From an approximate solution of the equations of motion a time constant is obtained for each mode. From a consideration of the fluid dynamics several methods are developed for determining the damping constant.
The coefficients in the partial fraction expansion considered are given by Heaviside's formula. The evaluation of the coefficients involves the differential of a quotient of two polynomials. A simplified approach for the evaluation of the coefficients is discussed. Leibniz rule is applied and a recurrence formula is derived. A coefficient can also be determined from a system of simultaneous equations. Practical methods for the performance of the computational operations involved in both approaches are considered.
Theorems and their proof are given for the solution of partial derivatives for various scaler functions of matrices.
A ring partially filled with a viscous fluid has been analyzed as a nutation damper for a spinning satellite. The fluid has been modelled as a rigid slug of finite length moving in a tube and resisted by a linear viscous force. It is shown that there are two distinct modes of motion, called the spin synchronous mode and the nutation synchronous mode. Time constants for each mode are obtained for both the symmetric and asymmetric satellite. The effects of a stop in the tube and an offset of the ring from the spin axis are also investigated. An analysis of test results is also given including a determination of the effect of gravity on the time constants in the two modes.
The spherical means of the solutions of a linear partial differential equation Lu = f in a conical region are studied. The conical region is bounded by a surface generated by curvilinear ti surfaces. The spherical mean is the average of u over a constant ti surface. The conditions on the linear differential operator, L, and on the orthogonal coordinates (ti, eta, zeta) are established so that the spherical mean of the solution subjected to the appropriate boundary and initial conditions can be determined directly as a problem with only space variable. Conditions are then established so that the spherical mean of the solution in one concial region will be proportional to that of a known solution in another conical region. Applications to various problems of mathematical physics and their physical interpretations are presented.
Results of nondestructive, partial alternating-field (a.f.) demagnetization studies of 40 meteorites weighing from 120 milligrams to 1.86 gram. Demagnetizing fields ranged up to 400 Oe. Results are given in the form of intensity curves and directional plots of alternating field demagnetization for carbonaceous meteorites, ordinary chondrites, and stony-irons.
The purpose of the present paper is to determine rigorously the effect of viscous dissipation on the stability and time-dependent motion of a spinning rigid body with a spherical cavity partially filled with liquid. The cavity is such that its center does not lie on the body axis of rotation. The work includes the problem formulation, consisting of the boundary-value problem for the liquid and moment equations for the entire system. Because of large Reynold's numbers involved, viscosity effects are negligible everywhere except for a thin boundary layer near the wetted surface. Using a boundary-layer analysis, the liquid problem is reduced to the solution of the inviscid equations subject to modified boundary conditions.
The steady-state solution to the full Navier-Stokes equations for complicated flows is generally difficult to obtain. The Burgers (1948) equation is used as a model of the Navier-Stokes equations. The steady-state solution is obtained by a one-step explicit technique resulting from a partial implicitization of the difference equation. Stability analysis shows that the technique is unconditionally stable, and numerical tests show the technique to be accurate.
This paper presents a technique for the partial-fraction expansion of functions which are ratios of polynomials with real coefficients. The expansion coefficients are determined by writing the polynomials as Taylor's series and obtaining the Laurent series expansion of the function. The general formula for the inverse Laplace transform is also derived.
Thrust-induced supercirculation effects from thrust vectoring have indicated a potential for not only increasing maneuverability of fighter aircraft but also as a means of improving cruise performance. The current study investigated a partial-span rectangular jet-exhaust nozzle located at the wing trailing edge that acts similar to a jet flap by increasing lift due to supercirculation. This paper summarizes experimental studies including the effects of nozzle deflection angle, wing camber, and nozzle shape and exit location on lift, drag and load distributions. The results indicate that significant increases in thrust-induced lift along with substantial decreases in drag are possible.
A collisional electromagnetic dispersion relation is derived from two-fluid theory for the interchange mode coupled to the Alfven, acoustic, drift and entropy modes in a partially ionized plasma. The fundamental electromagnetic nature of the interchange model is noted; coupling to the intermediate Alfven mode is strongly stabilizing for finite k sub z. Both ion viscous and ion-neutral stabilization are included, and it was found that collisions destroy the ion finite Larmor radius cutoff at short perpendicular wavelengths.
The structure of the drift instability was examined in several density regimes. Let sub e be the total electron mean free path, k sub z the wave-vector component along the magnetic field, and the ratio of perpendicular ion diffusion to parallel electron streaming rates. At low densities (k sub z lambda 1) the drift mode is isothermal and should be treated kineticly. In the finite heat conduction regime square root of m/M k sub z Lambda sub 1) the drift instability threshold is reduced at low densities and increased at high densities as compared to the isothermal threshold. Finally, in the energy transfer limit (k sub z kambda sub e square root of m/M) the drift instability behaves adiabatically in a fully ionized plasma and isothermally in a partially ionized plasma for an ion-neutral to Coulomb collision frequency ratio.
The net radiation method is developed for systems having both opaque and partially transparent walls. Heat convection is present at the surfaces and heat conduction through the windows is taken into account. Specific equations are derived for a window between two parallel plates, where one plate is at an elevated temperature typical of what would be encountered in an electric furnace, and the other plate is being cooled. A two-band model is used with cutoff wavelengths typical of glass or quartz. Numerical results are obtained for the window temperature and the heat flow through the window. The effect on these quantities of various plate temperatures and emissivities is shown.
The purpose of this paper is to show how the important problems of linear system theory can be solved concisely for a particular class of linear systems, namely block circulant systems, by exploiting the algebraic structure. This type of system arises in lumped approximations to linear partial differential equations. The computation of the transition matrix, the variation of constants formula, observability, controllability, pole allocation, realization theory, stability and quadratic optimal control are discussed. In principle, all questions which are solved here could also be solved by standard methods; the present paper clearly exposes the structure of the solution, and thus permits various savings in computational effort.
Certain Rydberg states and an intershell transition of atomic oxygen were shown to partially autoionize, and to produce emission spectra competitive with autoionization. These states are forbidden to autoionize on the basis of LS coupling; but they were observed both in emission spectroscopy and in photoelectron spectroscopy. The results explain an unidentified structure in the 584 Angstrom He I atomic O spectrum observed by previous investigators.
We discuss the gravity dependence of the Mg II resonance lines calculated with inclusion of effects of partial redistribution in frequency. Using chromospheric models scaled from a solar model, we demonstrate the increased decoupling of the radiation temperature of the k1 feature from the minimum electron temperature in lower-gravity models. The limb darkening of the k-line in the main-sequence model is also discussed.
An approach is presented for applying the net radiation method developed by Siegel and Howell (1972) and Sparrow and Cess (1966) to systems involving opaque and partially transmitting walls. The results obtained from the basic equations for various values of plate emissivities and temperatures are presented in graphs. Attention is given to the window temperature relative to the temperature of the hot wall and the heat transferred relative to that transferred without the window.
The stability and time dependent motion of a spinning satellite, simulated by a rigid body with a cavity partially filled with liquid is examined. The problem formulation, consisting of the boundary-value problem for the liquid and moment equations for the entire system is presented. Because of large Reynold's numbers involved, viscosity effects are negligible everywhere except for a thin boundary layer near the wetted surface. Using a boundary-layer analysis, the effect of the boundary layer is replaced by modified boundary conditions for the liquid. The solution of the differential equations for the inviscid problem is solved in closed form. A semi-analytical numerical solution of the inviscid equations subject to the viscous boundary condition has proved unsucessful.