A Class of Linear Functional Equations
Summary on autonomous linear functional equations
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Summary on autonomous linear functional equations
Maximum error curves for Lanczos selected point method of polynomial solution to ordinary differential equations, using Chebyshev and Legendre functions
Complete Rayleigh scattered field within homogeneous plane parallel atmosphere, noting scalar transfer equation extension
Feynman integral for classical waves evaluated, using Hamiltonian approach to summation
Integral stress function for state of membrane stress in shells of revolution formed by second- order surface
Functional expression for describing lunar surface directional reflectance characteristics
Integral representation theorems and weak compactness for bounded linear transformations of Banach and other spaces
Method of finite integral transforms as format for employment of incomplete eigenfunctions, discussing application of equitriangular transform
Optimal singular controls made nonsingular for decreasing epsilon values by adding integral quadratic functional of control to cost functional
A 90-day test is reported of a regenerative life support system which was completed in a space station simulator. The long duration of the test and the fact that it was manned, imposed rigid reliability and safety requirements on the facility. Where adequate reliability could not be built into essential facility systems, either backup systems or components were provided. Awareness was intensified by: (1) placing signs on every piece of equipment that could affect the test, (2) painting switches on all breaker panels a bright contrasting color, (3) restricting access to the test control area, and (4) informing personnel in the facility (other than test personnel) of test activities. It is concluded that the basic facility is satisfactory for conducting long-duration manned tests, and it is recommended that all monitor and alarm functions be integrated into a single operation.
A continuous flexible body nonlinear dynamics computer program is used for simulating the spinning mode performance of a spacecraft under applied control torques. The program takes into account the continuous flexible nature of the antennas by representing deflections in terms of shape functions and integrated the spatial dependence in the formulation of the equations of motion. Comparison of RAE flight data on roll, pitch, and yaw with predictions of the computer program in the gravity gradient mode show fair to good agreement in roll and pitch and excellent agreement in the yaw angle.
Emission from the exhaust plume of a 30 cm mercury ion thruster was measured from 160 to 600 nm as a function of axial and radial distance from the thruster discharge chamber. The spectrally dispersed absolute intensities were used to construct an empirical volume rate function. The function was integrated along a typical instrument field of view, and the resulting apparent brightness was compared with instrument sensitivities to evaluate the extent of optical interference. Most of the emitted radiation came from UV lines of excited mercury atoms and ions, with no observable continuum emission. The intensity levels degraded rapidly with distance from the thruster so that optical interference was negligible for fields of view not intercepting the beam axis. The operation of only one instrument, a zodiacal photopolarimeter, was considered incompatible with simultaneous thruster operation.
The baseline avionics systems for the space tug is comprised of a central digital computer that integrates the functions of all of the tug's subsystems by means of a redundant digital data bus. The major subsystems of the avionics system are: data management; communications; guidance, navigation, and control; rendezvous and docking; electrical power; and instrumentation. The baseline avionics system for the space tug resulting from system and subsystem trade studies is defined. Tug interfaces with the spacecraft, orbiter and the ground, and the baseline philosophy and configuration for onboard checkout of the tug are included. Baseline configurations, functional and operational features, component details and characteristics, and the supporting software are included in the subsystem descriptions.
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Emission from the exhaust plume of a 30 cm mercury ion thruster was measured from 160 to 600 nm as a function of axial and radial distance from the thruster discharge chamber. The spectrally dispersed absolute intensities were used to construct an empirical volume emission rate function. The function was integrated along a typical instrument field of view, and the resulting apparent brightness was compared with instrument sensitivities to evaluate the extent of optical interference. The intensity levels degraded rapidly with distance from the thruster so that optical interference was negligible for fields of view not intercepting the beam axis. The operation of only one instrument, a zodiacal photopolarimeter was considered incompatible with simultaneous thruster operation.
The development is discussed of analytical techniques and numerical methods for the prediction of the stability behavior of liquid propellant rocket combustors with partial length acoustic liners, injector face baffles, and nonlinear combustion responses. Three primary objectives included: (1) extension of the Green's Function integral-iteration technique previously developed so that nonlinear three dimensional wave propagation effects could be included in stability predictions; (2) development of an analytical technique and a computer program for the prediction of the damping effects caused by injector face baffles; and (3) inclusion of a nonlinear, wave distortation dependent, combustion response model in the global stability analysis and determination of its effect on combustor stability.
The rotational energy is separated from vibrational energy in the two-particle, steady-state wave equation and to first order the solutions are harmonic oscillator functions. The classical phase integral gives a partition function valid only at high temperature, but the quantum summation is easily performed to give analytic expressions for all the thermodynamic properties of the harmonic oscillator at all temperatures. Anharmonic effects are treated by small perturbation solutions to the wave equation and the relation between energy levels and a series expansion of the perturbation potential is derived. Next, the quantum solutions for an oscillator with a Morse-function potential are derived in terms of Laguerre polynomials.
A shear flow aerodynamic theory for steady incompressible flows is presented for both the lifting and non lifting problems. The slow variation of the boundary layer thickness is considered. The slowly varying behavior is treated by using multitime scales. The analysis begins with the elementary wavy wall problem and, through Fourier superpositions over the wave number space, the shear flow equivalents to the aerodynamic transfer functions of classical potential flow are obtained. The aerodynamic transfer functions provide integral equations which relate the wall pressure and the upwash. Computational results are presented for the pressure distribution, the lift coefficient, and the center of pressure travel along a two dimensional flat plate in a shear flow. The aerodynamic load is decreased by the shear layer, compared to the potential flow. The variable thickness shear layer decreases it less than the uniform thickness shear layer based upon equal maximum shear layer thicknesses.