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Scalar measure of system sensitivity to plant parameter variations applied to design of linear lumped stationary multivariable feedback control systems
Microscopic particle mass spectra in six dimensional scalar, spinor and vector fields, noting cosmological implications and eight dimensional theory
Orbiting gyroscope de Sitter precession in different versions of Brans-Dicke theory, discussing term arising from anomalous scalar force in equations of motion
Independent noise driven nonlinear dynamic systems identification, performing linear discrete-time scalar measurements
Neutral functional equation including scalar differential-difference equation, determining sufficient conditions for zero solution
Antennas are described with gravitational radiation properties such as polarization, directivity, and scalar and tensor characteristics. These antenna devices are mechanically resonant systems in the shape of a hollow square with fundamental frequencies in the Hz range. An antenna characteristic is that the absorption cross section for quadrupole radiation at the normal frequency of vibration is the same as that of the fundamental if the damping factors are the same. The absorption cross section of quadrupole gravitational radiation is calculated for a class-1 detector of a cylindrical cross section and for a class-2 detector shaped like a hollow square.
The near field antenna pattern of an obstructed optical transmitter, such as a Cassegrainian telescope, has been computed using the Fresnel approximation to the scalar diffraction integral. A number of cases have been considered. These include uniformly illuminated, obstructed circular apertures, and apertures coherently illuminated with a divergent gaussian beam wave. Other beam profiles that may be derived by energy redistribution of the laser beam have also been considered. The techniques used for the numerical evaluation of the Fresnel integral are discussed and results for the optical systems to be used on the High Altitude Aircraft Optical Communications Experiment are presented.
The dynamic characteristics of two-stage slender elastic body were investigated. The first stage, containing a solid-fuel rocket, possesses variable mass while the second stage, envisioned as a flexible case, contains packaged instruments of constant mass. The mathematical formulation was in terms of vector equations of motion transformed by a variational principle into sets of scalar differential equations in terms of generalized coordinates. Solutions to the complete equations were obtained numerically by means of finite difference techniques. The problem has been programmed in the FORTRAN 4 language and solved on an IBM 360/50 computer. Results for limited cases are presented showing the nature of the solutions.
A modeling approach, which utilizes a matrix of transfer functions to describe the human pilot in multiple input, multiple output control situations, is studied. The approach used was to extend a well established scalar Wiener-Hopf minimization technique to the matrix case and then study, via a series of experiments, the data requirements when only finite record lengths are available. One of these experiments was a two-controller roll tracking experiment designed to force the pilot to use rudder in order to coordinate and reduce the effects of aileron yaw. One model was computed for the case where the signals used to generate the spectral matrix are error and bank angle while another model was computed for the case where error and yaw angle are the inputs. Several anomalies were observed to be present in the experimental data. These are defined by the descriptive terms roll up, break up, and roll down. Due to these algorithm induced anomalies, the frequency band over which reliable estimates of power spectra can be achieved is considerably less than predicted by the sampling theorem.
Data on atmospheric pressure, density, temperature and winds between 50 and 200 km were collected from sources including Meteorological Rocket Network data, ROBIN falling sphere data, grenade release and pitot tube data, meteor winds, chemical release winds, satellite data, and others. These data were analyzed by a daily difference method and results on the distribution statistics, magnitude, and spatial structure of the irregular atmospheric variations are presented. Time structures of the irregular variations were determined by the analysis of residuals from harmonic analysis of time series data. The observed height variations of irregular winds and densities are found to be in accord with a theoretical relation between these two quantities. The latitude variations (at 50 - 60 km height) show an increasing trend with latitude. A possible explanation of the unusually large irregular wind magnitudes of the White Sands MRN data is given in terms of mountain wave generation by the Sierra Nevada range about 1000 km west of White Sands. An analytical method is developed which, based on an analogy of the irregular motion field with axisymmetric turbulence, allows measured or model correlation or structure functions to be used to evaluate the effective frequency spectra of scalar and vector quantities of a spacecraft moving at any speed and at any trajectory elevation angle.
A compiler for recognizing statements of a FORTRAN program which are suited for fast execution on a parallel or pipeline machine such as Illiac-4, Star or ASC is described. The technique employs interval analysis to provide flow information to the vector/parallel recognizer. Where profitable the compiler changes scalar variables to subscripted variables. The output of the compiler is an extension to FORTRAN which shows parallel and vector operations explicitly.
The rubidium vapor magnetometer data of the scalar magnetic-field intensity obtained by the OGO 3 and 5 satellites are analyzed to study the magnetospheric-field distortions in terms of the observed field magnitude under quiet and slightly disturbed conditions minus the magnitude of the reference geomagnetic field (delta B). Average contours of equal delta Bs are shown in the geomagnetic noon-midnight and dawn-dusk meridian planes for magnetically quiet and slightly disturbed conditions. The equatorial distribution of observed delta Bs as a function of geocentric distance differs substantially from that expected from the well-known models of the quiet-time ring current. Other findings suggest that there must be a population of low-energy particles with substantial total energy near the equator at distances of 2 to 5 earth radii that has not been recognized as having sufficient energy to inflate the magnetic field.
Application of optimal control theory to practical problems has been limited by the difficulty of prescribing a performance index which accurately reflects design requirements. The task of deriving equivalent performance indices is considered in the present paper for a plant that is a completely controllable, scalar linear system with state feedback. A quadratic index is developed which leads to an optimal design performance satisfying some of the classical performance criteria.
Optimum bounding filters are derived for a specific version (steady state time-invariant with scalar observations) of the Kalman-Bucy filtering problem with inexactly known system parameters and for the Wiener filtering problem with inexactly known spectral densities. The designed filter obtains a bound on the actual error covariance which is not known, and it also prevents apparent divergence. Conditions are derived for the design of the optimum bounding filter within a permissible class of solutions; this turns out to be the min-max mean-square error filter for an extended class of solutions. The bounding filter can be of lower order than the original system, and a technique is devised for reducing the order of the filtering system and concurrently obtaining a figure of merit for its performance.
A review of exact techniques for determining the surface of a three-dimensional perfectly conducting body is given, followed by some new results on the uniqueness question concerning the number of measurements that may be required to explicitly determine the surface of the body. It is then shown that the inhomogeneous but spherically symmetric dielectric electromagnetic case is reducible to a scalar inverse problem that can be treated by known techniques.
Proton recoil distributions were obtained by using organic liquid scintillators of different size. The measured distributions are converted to neutron spectra by differentiation analysis for comparison to the unfolded spectra of the largest scintillator. The approximations involved in the differentiation analysis are indicated to have small effects on the precision of neutron spectra measured with the smaller scintillators but introduce significant error for the largest scintillator. In the case of the smallest cylindrical scintillator, nominally 1.2 by 1.3 cm, the efficiency is shown to be insensitive to multiple scattering and to the angular distribution to the incident flux. These characteristics of the smaller scintillator make possible its use to measure scalar flux spectra within media high efficiency is not required.
The percentage levels of wind speed differences are presented computed from sequential FPS-16 radar/Jimsphere wind profiles. The results are based on monthly profiles obtained from December 1964 to July 1970 at Cape Kennedy, Florida. The profile sequences contain a series of three to ten Jimspheres released at approximately 1.5-hour intervals. The results given are the persistence analysis of wind speed difference at 1.5-hour intervals to a maximum time interval of 12 hours. The monthly percentage of wind speed differences and the annual percentage of wind speed differences are tabulated. The percentage levels are based on the scalar wind speed changes calculated over an altitude interval of approximately 50 meters and printed out every 25 meters as a function of initial wind speed within each five-kilometer layer from near sea level to 20 km. In addition, analyses were made of the wind speed difference for the 0.2 to 1 km layer as an aid for studies associated with take-off and landing of the space shuttle.
The space-time integral of the thermodynamic pressure plays the role of the thermodynamic potential for compressible, adiabatic flow in the sense that the pressure integral for stable flow is less than for all slightly different flows. This stability criterion can be converted into a variational minimum principle by requiring the molar free-enthalpy and the temperature, which are the arguments of the pressure function, to be generalized velocities, that is, the proper-time derivatives of scalar spare-time functions which are generalized coordinates in the canonical formalism. In a fluid context, proper-time differentiation must be expressed in terms of three independent quantities that specify the fluid velocity. This can be done in several ways, all of which lead to different variants (canonical transformations) of the same constraint-free action integral whose Euler-Lagrange equations are just the well-known equations of motion for adiabatic compressible flow.