Telecommunications Division fourth harmonic power analyzer
A microprocessor-based instrumentation system was developed to be used in the measurement and analysis of fourth harmonic power generated by the DSN high-power transmitters.
Foster, C.↗
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Optimization of continuous one-dimensional structures under steady harmonic excitation
The paper examines some questions relating to the optimal design of continuous one-dimensional structures driven by harmonically oscillating loads. Optimal-control methods are applied to a cantilever bar driven sinusoidally by an axial force at its tip to illustrate the minimum-weight design of one-dimensional structures under dynamic excitation. Realistic constraints are imposed during the optimizations, including a maximum allowable stress amplitude at any point along the bar and a minimum cross-sectional area. It is shown that in the absence of damping, the design space may contain many disjoint feasible regions, and multiple optima can exist. Detailed solutions are obtained for continuous bars with an excitation frequency less than, and then greater than, the fundamental free-vibration frequency. It is found that above a certain excitation frequency, two or more arcs with different constraints characterize the optimal designs. It is concluded that when more than two different constrained arcs characterize the optimal solution, the continuum approach may be impractical, and finite-element approximations may offer the only alternative.
Johnson, E. H.↗
Automated fourth-harmonic analyzer
The final design of a field portable microprocessor-based, microwave measuring and analysis instrument to be used for S-band transmitter fourth-harmonic power analysis and its impact on X-band reception in a dual S-X-band system is described.
Foster, C. F.↗
A 230-GHz radiometer system employing a second-harmonic mixer
A radiometer system for use in the 1.3 mm region has been constructed and used for radio astronomical observations. A second-harmonic mixer employing a single Schottky diode downconverts the incident power to an IF frequency of about 1400 MHz. The measured double-sideband system noise temperature is 6000 K (noise figure = 13 dB) and the double-sideband mixer conversion loss is calculated to be 10 dB. The mixer is tunable over a range of at least 15 GHz.
Goldsmith, P. F.↗
Higher harmonic rotor blade pitch control
Tests of a model 'Reverse Velocity Rotor' system at high advance ratios and with twice-per-revolution cyclic pitch control were made under joint Navy-NASA sponsorship in the NASA, Ames 12 ft. pressure tunnel. The results showed significant gains in rotor performance at all advance ratios by using twice-per-revolution control. Detailed design studies have been made of alternative methods of providing higher harmonic motion including four types of mechanical systems and an electro-hydraulic system. The relative advantages and disadvantages are evaluated on the basis of stiffness, weight, volume, reliability and maintainability.
Ewans, J. R.↗
Comparison of results obtained by solving the radiative transfer equation with an iterative method and a spherical harmonics method
Fluxes and intensities of light scattered by a model atmosphere are computed by a spherical harmonics approximation and by an iterative method of solving the radiative transfer equation and are compared. The large differences in the net fluxes and intensities reported by Dave and Armstrong (1974) for the two methods are reduced here by making a few changes in the iterative routine. Decreasing the polar angle increment from 2 to 1 deg in the iterative method of computing the source function does not improve the results as suggested by Dave and Armstrong.
Bahethi, O. P.↗
Lunar gravity - A harmonic analysis
A sixteenth-degree and sixteenth-order spherical harmonic lunar gravity field has been derived from the long-term Keplerian variations in the orbits of the Apollo subsatellites and Lunar Orbiter 5. This model resolves the major mascon gravity anomalies of the lunar near side and is in very good agreement with line-of-sight acceleration results. The far-side map shows the major ringed basins to be strong localized negative anomalies located in broad regions of positive gravity which correspond closely to the highlands. The rms pressure levels calculated from equivalent-surface height variations show that the moon and earth support nearly equal pressures, whereas Mars is appreciably stronger. The moon appears to support larger loads than earth owing to its weaker central gravity field and perhaps a colder upper lithosphere. Significant differences between the low-degree gravity and topography spectra indicate that the longer-wavelength topographic features are isostatically compensated.
Ferrari, A. J.↗
Third-order nonlinearities in molecular hydrogen - Two-photon resonance enhanced third-harmonic generation and Raman scattering
Effects of quantum mechanical interferences on third-order susceptibilities in molecules are studied. First principle calculations for molecular hydrogen are presented and shown to agree with results derived from experimental stimulated Raman gain and spontaneous Raman cross-section data. 10 percent third-harmonic conversion efficiency in H2 at 1 atm without phase matching should require a 150 MW per sq cm at 4.81 microns. As little as 5.9-MW power is sufficient when the beam is properly focused. Resonance Raman scattering (RRS) is proposed for experimentally investigating the interference effects, which tend to reduce the strength of third-order nonlinear susceptibilities.
Pan, C.-L.↗
Direct method for solving transfer equation by expansion in spherical harmonics: Scattering in atmosphere with Lambertian lower boundary and thermal radiation transfer
The direct method for the solution of the spherical harmonics approximation to the equation of transfer of radiation is applied to the cases of (1) scattering of the solar radiation in the atmosphere with the Lambertian boundary and (2) thermal radiation transfer.
Ustinov, Y. A.↗
Possible measurement of the coefficient of the second zonal harmonic of the sun's gravitational field with a solar probe
The use of radio tracking of a solar probe to estimate accurately the coefficient of the second zonal harmonic of the sun's gravitational field was examined. Preliminary results indicate that the coefficient can be estimated with a standard error of 10 to the minus 8th power or less, provided that the probe is equipped with a suitable drag-free system to compensate for the effects of non-gravitational accelerations. For signal paths that pass near the sun, dual-band ranging to the probe can provide the tracking accuracy needed to insure that the standard of error is equal to or less than 10 to minus 8th power. The possibility of achieving such accuracy with a single-band radio uplink and a dual-band downlink is discussed.
Reasenberg, R. D.↗
The relationship between mean anomaly block sizes and spherical harmonic representations
The frequently used rule specifying the relationship between a mean gravity anomaly in a block whose side length is theta degrees and a spherical harmonic representation of these data to degree l-bar is examined in light of the smoothing parameter used by Pellinen (1966). It is found that if the smoothing parameter is not considered, mean anomalies computed from potential coefficients can be in error by about 30% of the rms anomaly value. It is suggested that the above mentioned rule should be considered only a crude approximation.
Rapp, R. H.↗
Gravitational harmonics from shallow resonant orbits
Gravitational constraint (lumped coefficient) equations are derived from GEOS-2 data and a detailed analysis of the shallow resonance problem. The equations follow from elementary perturbation theory and show that all such lumped coefficients are harmonic in the argument of perigee. The best along-track constraints derived from them account for all but about 2% of the 13th-order resonant information in the tracking data. The equations are also in good agreement with recent comprehensive gravity models which use substantial amounts of GEOS-2 data.
Wagner, C. A.↗
Mars topography harmonics and geophysical implications
The paper describes an improved model of Martian global topography which has been obtained by fitting a sixteenth-degree harmonic series to occultation, radar, spectral, and photogrammetric measurements. Empirical elevation data based on photographic data are used to supplement the observations in areas without data. Values for the mean radius, the mean density, and the displacement of the center of the figure from the center of mass are presented. The reported geometric flattening is too great and the reported dynamic flattening is too small for Mars to be homogeneous and hydrostatic. Maps of the data distribution, global topography, and Bouguer gravity anomaly are interpreted in terms of a crustal thickness map which is consistent with gravity, topography, and recent preliminary Viking seismic results.
Bills, B. G.↗
Incompressible fluid ellipsoids in halos. I - The second-harmonic oscillations of the Maclaurin spheroids
The structure and stability of Maclaurin spheroids embedded in rigid uniform-density oblate spheroidal halos are determined by the tensor virial-equation method. These spheroid-halo systems can be thought of as crude fluid analogs of disk galaxies with halos. The halos are assumed to have the same center, the same axis of symmetry, and the same equatorial radius as the Maclaurin spheroids. Only halos with lower eccentricity than the Maclaurin spheroids are considered. The dynamic instability of the toroidal (barlike) modes is suppressed when m, the ratio of the halo mass to Maclaurin spheroid mass, is greater than 3 pi/8 for spherical halos and when m is greater than 1/2 for halos congruent to the Maclaurin spheroids. Intermediate halo flattenings yield intermediate critical m-values. On the other hand, a neutral point of the toroidal modes in the rotating and inertial frames occurs for all m and for all allowed halo flattenings. Growth rates for secular instability beyond the neutral point are calculated, and the eigenfrequencies of all second-harmonic modes are given for select cases. The Ostriker-Peebles (1973) conjecture concerning the stability of disk galaxies against barlike perturbations appears to be incorrect.
Durisen, R. H.↗
Quantum nondemolition measurements of harmonic oscillators
Measuring systems to determine the real component of the complex amplitude of a harmonic oscillator are described. This amplitude is constant in the absence of driving forces, and the uncertainty principle accounts for the fact that only the real component can be measured precisely and continuously ('quantum nondemolition measurement'). Application of the measuring systems to the detection of gravitational waves is considered.
Thorne, K. S.↗
A procedure for analyzing transonic flow over harmonically oscillating airfoils
Finite difference procedures were successfully used to solve the steady transonic flow about airfoils and appear to provide a practical means for calculating the corresponding unsteady flow. The purpose of the paper is to describe a finite difference procedure derived from the equations for the potential flow by assuming small perturbations and harmonic motion. The velocity potential is divided into steady and unsteady parts, and the resulting unsteady equation is linearized on the basis of small amplitudes of oscillation. The steady velocity potential, which must be calculated first, is described by the classical nonlinear transonic differential equation.
Weatherill, W. H.↗
Spherical harmonic analysis for verfication of a global atmospheric model
Surface spherical harmonics were used to analyze the horizontal fields of various quantities generated by a global climate model. Also, the computed monthly mean forecast fields were compared with the corresponding observed fields.
Christidis, Z.↗
Random harmonic analysis program, L221 (TEV156). Volume 2: Supplemental system design and maintenenace document
Volume 2 of a two volume document is presented. A computer program, L222 (TEV 156), available for execution on the CDC 6600 computer is described. The program is capable of calculating steady-state solutions for linear second-order differential equations due to sinusoidal forcing functions. From this, steady-state solutions, generalized coordinates, and load frequency responses may be determined. Statistical characteristics of loads for the forcing function spectral shape may also be calculated using random harmonic analysis techniques. The particular field of application of the program is the analysis of airplane response and loads due to continuous random air turbulence.
Graham, M. L.↗