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The identification of the mass, damping and stiffness matrix for the finite-element formulation of a structure will be given. It will be shown that the quadrature integration procedure can be used to find the desired matrices when reasonable assumptions hold. The mass, damping and stiffness matrices of the matrix polynomial are identified by the algorithm.
The two body problem was analyzed with a specific drag model. The model treats drag as a force proportional to the vector velocity and inversely proportional to the distance to the center of attraction. The solution is expressed in terms of known functions and is of a simple and compact form. The time of flight is expressed as a quadrature in the true anomaly. The results are: (1) development of a vector differential equation which allows analysis of an infinite number of gravitational and drag models; and (2) obtaining the solution of a linear differential equation using the inverse method of laplace transforms.
A total of five high and ten low dispersion UV spectra of the interacting contact binary SV Centauri obtained between 1979 and 1982 are analyzed. The low resolution observations cover the whole phase range, while a few selected phases were observed in high dispersion. The UV data were complemented with optical photometric and spectroscopic observations, in order to determine the tructure and absolute dimensions of the system. The profiles of prominent UV resonance and metastable lines undergo drastic changes with phase angle and time. Their overall appearance indicates relatively strong mass loss from the system, exhibiting pronounced variations of the stellar wind. The far UV continuum distribution suggests the presence of a luminous hot radiation source with maximum emission in the soft X-ray range, which is most apparently seen during the first quadrature phase, while it is weakest close to primary minimum. The case exchange and mass loss process as well as the evolutionary stage of SV Centauri are discussed.
An alternative to rectification is proposed for detection of an ultrasonic signal. This method is especially useful in medical and non-destructive evaluation (nde) applications. With this method, the magnitude of the complex analytic signal is used to define the envelope of the ultrasonic waveform. The square of this quantity has been shown elsewhere to be equal to the true rate-of-arrival of energy. An earlier study, using digital data processing, has already demonstrated the superior resolvability of closely spaced interfaces obtained with the analytic signal magnitude, as compared to conventional rectification. Here, an analogue implementation is presented which utilizes single-sideband techniques to obtain both quadrature components of the analytic signal and its magnitude. A conventional transducer, pulser, and receiver are used.
The radiative transfer theory is applied to a random medium for the case of passive remote sensing. A general numerical solution with Gaussian quadrature method is studied. For a medium with laminar structure or a medium with cylindrical structure, closed form solutions are obtained by solving the radiative transfer equations of a two-layer random medium. Numerical results for the general case and the two limiting cases are compared.
A simple method for calculating the unsteady aerodynamic loadings on harmonically oscillating thin wings in subsonic flow has been developed. The method is based on a concept of concentrated lift forces. The wing is divided into the element surfaces on which lift distributions are represented by single concentrated lift forces. Since the procedure does not include any quadratures, it can be applied easily to calculate the unsteady aerodynamic loadings on complex planform wings even when they have partial span control surfaces. Numerical calculations are carried out for various wing geometries and compared with other analyses and experiments.
Attention is given to two real integral functions which occur in the kernel of singular integral equations for subsonic unsteady lifting surfaces. The arguments k, r, and X of the functions correspond to the reduced frequency, spanwise distance, and modified coordinate in the flow direction, respectively. The value of the parameter nu in the functions depends on geometrical conditions. The considered investigation has the objective to present a series for general values of the nonnegative integer nu in order to compute efficiently the integral functions. The approach makes it possible to avoid any approximation or numerical quadrature.
Serial minimum-shift keyed (MSK) modulation, a technique for generating and detecting MSK using series filtering, is ideally suited for high data rate applications provided the required conversion and matched filters can be closely approximated. Low-pass implementations of these filters as parallel inphase- and quadrature-mixer structures are characterized in this paper in terms of signal-to-noise ratio (SNR) degradation from ideal and envelope deviation. Several hardware implementation techniques utilizing microwave devices or lumped elements are presented. Optimization of parameter values results in realizations whose SNR degradation is less than 0.5 dB at error probabilities of .000001.
Bandwidth efficient digital modulation techniques, proposed for use on and/or applied to satellite channels, are reviewed. In a survey of recent works on digital modulation techniques, the performance of several schemes operating in various environments are compared. Topics covered include: (1) quadrature phase shift keying; (2) offset - QPSK and MSK; (3) combined modulation and coding; and (4) spectrally efficient modulation techniques.
A stability study of rotor/bearing systems is presented. Even though it was limited to study of a fully lubricated bearing subject to oil whirl, and further limited to low eccentricity region for linearity and with only one type of lubricant, it can be seen that the perturbation methodology, together with the sorting of the impedance terms into direct and quadrature with respect to input force can be very useful to the general study of stability. Further, the concept of active feedback should assist to increase knowledge in rotor system stability. While there remains a large amount of study to be accomplished, perhaps some more tools are available to assist this field of analysis.
A method is presented for performing efficient and stable finite element calculations of heat conduction with quadrilaterals using one-point quadrature. The stability in space is obtained by using a stabilization matrix which is orthogonal to all linear fields and its magnitude is determined by a stabilization parameter. It is shown that the accuracy is almost independent of the value of the stabilization parameter over a wide range of values; in fact, the values 3, 2, and 1 for the normalized stabilization parameter lead to the 5-point, 9-point finite difference, and fully integrated finite element operators, respectively, for rectangular meshes and have identical rates of convergence in the L2 norm. Eigenvalues of the element matrices, which are needed for stability limits, are also given. Numerical applications are used to show that the method yields accurate solutions with large increases in efficiency, particularly in nonlinear problems.
A real-time signal processor was developed for the NASA/JSC L-and C-band airborne radar scatterometer sensor systems. The purpose of the effort was to reduce ground data processing costs. Conversion of two quadrature channels of data (like and cross polarized) was made to obtain Power Spectral Density (PSD) values. A chirp-z transform (CZT) approach was used to filter the Doppler return signal and improved high frequency and angular resolution was realized. The processors have been tested with record signals and excellent results were obtained. CZT filtering can be readily applied to scatterometers operating at other wavelengths by altering the sample frequency. The design of the hardware and software and the results of the performance tests are described in detail.
In passive microwave remote sensing of the earth, a theoretical model that utilizes the radiative transfer equations was developed to account for the volume scattering effects of the vegetation canopy. Vegetation canopies such as alfalfa, sorghum, and corn are simulated by a layer of ellipsoidal scatterers and cylindrical structures. The ellipsoidal scatterers represent the leaves of vegetation and are randomly positioned and oriented. The orientation of ellipsoids is characterized by a probability density function of Eulerian angles of rotation. The cylindrical structures represent the stalks of vegetation and their radii are assumed to be much smaller than their lengths. The underlying soil is represented by a half-space medium with a homogeneous permittivity and uniform temperature profile. The radiative transfer quations are solved by a numerical method using a Gaussian quadrature formula to compute both the vertical and horizontal polarized brightness temperature as a function of observation angle. The theory was applied to the interpretation of experimental data obtained from sorghum covered fields near College Station, Texas.
An analytic solution to the two-body problem with a specific drag model is obtained. The model treats drag as a force proportional to the vector velocity and inversely proportional to the square of the distance to the center of attraction. The solution is expressed in terms of known functions and is of a simple and compact form. The time-of-flight is expressed as a quadrature in the 'true anomaly'.
Because the dynamical nonequilibrium of closely packed twisted flux tubes is essentially the problem of two-dimensional MHD turbulence, the extensive literature on two-dimensional turbulence represents the hydrodynamics of magnetic nonequilibrium. Many features of the turbulence can conversely be understood as a consequence of the dynamical nonequilibrium. Attention is presently given to the dynamics of the strong fluid jets, issuing from reconnection points, that are exhibited by numerical simulations of two-dimensional turbulence. Simple examples are given which show that the uniformity of jet width observed is a consequence of the form of the pressure of the magnetic fields between which the jets are confined. The general hydrodynamics of a layer of fluid confined by steady pressures is reducible to a quadrature, so that a variety of effects may be considered, including gravitation. The dissipation of the solar corona is discussed.
The aerodynamics of propellers and rotors is especially complicated because of the highly three-dimensional and compressible nature of the flow field. However, in linearized theory the problem is governed by the wave equation, and a numerically-efficient integral formulation can be derived. This reduces the problem from one in space to one over a surface. Many such formulations exist in the aeroacoustics literature, but these become singular integral equations if one naively tries to use them to predict surface pressures, i.e., for aerodynamics. The present paper illustrates how one must interpret these equations in order to obtain nonambiguous results. After the regularized form of the integral equation is derived, a method for solving it numerically is described. This preliminary computer code uses Legendre-Gaussian quadrature to solve the equation. Numerical results are compared to experimental results for ellipsoids, wings, and rotors, including effects due to lift. Compressibility and the farfield boundary conditions are satisfied automatically using this method.
Both passive and active remote sensing of atmospheric precipitation are studied with the vector radiative transfer equations by making use of the Mie scattering phase functions and incorporating the raindrop-size distributions. For passive remote sensing, the Gaussian quadrature method is employed to solve for the brightness temperatures. For active remote sensing, an iterative approach carrying out to the second order in albedo is used to calculate for the bistatic coefficients, the backscattering cross sections/unit volume, and the interchannel cross talks. The calculated results are plotted as a function of rainfall rates and compared to various available experimental data. The theoretical model is easily applied to the remote sensing of aerosol particles, smoke, fog, and haze at infrared and visible frequencies.
Voltage-controlled oscillator in suppressed-carrier detector acquire carrier frequency and phase quickly with help of frequency-discriminator arrangement. To obtain discriminator function, filter bandwidth in quadrature (Q) leg of detector is widened with respect to bandwidth of filter in inphase (l) leg.