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At least 109 records · Page 6

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NASA NTRS1973

The physical librations of the moon, including higher harmonic effects

The equations of the physical libration of the moon are developed using a representation of the earth-moon orbit as a Kepler ellipse referred to the lunar equator and expanding the lunar potential in terms of these Kepler elements. The Improved Lunar Ephemeris is used to calculate solar perturbations, and a linear integration of all effects arising from lunar gravitational harmonics through the fourth degree is performed. Aside from unobservable constant offsets of the principal axes, the main effects of the higher harmonics on longitude are: 10-sec six-yearly (argument omega), 1.2-sec three-yearly, 0.5-sec annual, and 0.1-sec monthly; on pole direction they are on the order of 0.5-sec six-yearly and 1.0-sec monthly. The higher harmonics must hence be taken into account in analyzing ranging data of 10 cm accuracy.

Kaula, W. M.↗

NASA NTRS1975

Type III solar radio bursts and the fundamental-harmonic hypothesis

The observational evidence is reviewed for the occurrence of type III solar radio bursts in pairs with frequency ratio two to one. We show that the observations can be explained under the hypothesis that there is a tendency for a type III burst to be followed by a second burst within approximately one second. This explanation leads to fewer difficulties than the hypothesis that type III bursts occur in pairs, one member being emitted at the fundamental of the local coronal plasma frequency, the other at its second harmonic. We conclude that in general, type III bursts are emitted at the second harmonic of the plasma frequency and that type III theories should account for this and only under very special circumstances (which are rare) for the emission at the fundamental and the second harmonic.

Rosenberg, H.↗

NASA NTRS1976

Disjoint design spaces in the optimization of harmonically excited structures

The paper deals with a method of optimizing harmonically or dynamically excited structures which removes the frequency constraint (that specifies that the structure's first natural frequency of vibration must be greater than the excitation frequency), replaces the displacement constraint by an inequality constraint on the allowable stress and applies finite element approximations to the continuous one-dimensional structures. When the problem is posed in this manner, the feasible design space is disconnected or 'disjoint'. An attempt is made to explain this disjointness by studying the optimal design of a thin-walled cantilevered rod subjected to steady, simple harmonic torsional excitation. The finite element method is applied to the optimization of a harmonically excited structure with an arbitrary number of design variables, with the disjointness of the design space, a complicating factor.

Johnson, E. H.↗

NASA NTRS1978

The polarization of second harmonic plasma emission

It is shown that second-harmonic plasma emission is partially polarized in the sense of the ordinary mode of magnetoionic theory only when the Langmuir waves are confined to a small range of angles (less than 30 deg) to the magnetic-field lines. Consequently, Suzuki and Sheridan's (1977) observations of the polarization of harmonic Type III emission implies that (at least in the cases reported) the Langmuir waves must be nearly one-dimensional. For a nearly one-dimensional distribution, the degree of polarization and the frequency of observation should be related to the magnetic field. For the observed polarization of Type III bursts, the implied magnetic-field strengths are strong enough for induced scattering to cause the Langmuir waves to become nearly one-dimensional, which is consistent with the observed sense of polarization. In other applications of harmonic plasma emission where the Langmuir waves might be isotropic or in a loss-cone distribution, polarization in the sense of the extraordinary mode is predicted.

Melrose, D. B.↗

NASA NTRS1978

Solitons and second harmonic radiation in type III bursts

The emission at the second harmonic of the plasma frequency from self-consistent Langmuir solitons is calculated. The theory predicts, in a natural way, the observed transition from the region where the intensity is linearly proportional to the electron flux to the region where the radio intensity is proportional to the square of the electron flux. A detailed comparison of the radiation observed at the second harmonic for the burst of 18:10 UT March 31, 1976, with the one expected on the assumption of radiation from solitons, using the correlated in situ measurements of the electric fields at the second harmonic, and their spatial structure, provides strong evidence that, for the first time, Langmuir solitons have been observed in space.

Papadopoulos, K.↗

NASA NTRS1978

On methods for application of harmonic control

The paper presents data which confirm the effectiveness of higher harmonic blade pitch control in substantially reducing helicopter rotor vibratory hub loads. The data are the result of recent tests on a 2.7-m model conducted in the Langley Research Center's transonic dynamics wind tunnel. Several predictive analyses developed in support of the NASA program are shown capable of accurately predicting both amplitude and phase of the higher harmonic control input required to nullify a single 4/rev force or moment input. The use of multiple blade feathering inputs in the design of a flightworthy higher harmonic control system is discussed.

Wood, E. R.↗

NASA NTRS1980

Spherical harmonic analysis of a synoptic climatology generated with a global general circulation model

Spherical harmonic analysis was used to analyze the observed climatological (C) fields of temperature at 850 mb, geopotential height at 500 mb, and sea level pressure. The spherical harmonic method was also applied to the corresponding "model climatological" fields (M) generated by a general circulation model, the "GISS climate model." The climate model was initialized with observed data for the first of December 1976 at 00. GMT and allowed to generate five years of meteorological history. Monthly means of the above fields for the five years were computed and subjected to spherical harmonic analysis. It was found from the comparison of the spectral components of both sets, M and C, that the climate model generated reasonable 500 mb geopotential heights. The model temperature field at 850 mb exhibited a generally correct structure. However, the meridional temperature gradient was overestimated and overheating of the continents was observed in summer.

Christidis, Z. D.↗

NASA NTRS1982

Sensitivity of selected geomagnetic properties to truncation level of spherical harmonic expansions

The model dependence of Gauss coefficients associated with a lack of spherical harmonic orthogonality on a nonuniform Magsat data grid is shown to be minor, where the fitting level exceeds the harmonic order by a value of approximately four. The shape of the magnetic energy spectrum outside the core, and the sensitivity to truncation level of magnetic contour location and the number of their intersections on the core-mantle boundary, suggest that spherical harmonic expansions of the main geomagnetic field should be truncated at a truncation level value of not more than eight if they are to be extrapolated to the core.

Benton, E. R.↗

NASA NTRS1982

Standing hydromagnetic waves observed by ISEE 1 and 2 - Radial extent and harmonic

Direct measurements of the spatial extent of the resonant hydromagnetic waves associated with Pc 4 and 5 magnetic pulsations made by the closely spaced ISEE 1 and 2 satellites are presented together with ISEE 1 determinations of the harmonic of the resonant waves. The use of two satellites in similar orbits, which makes it possible to distinguish between spatial and temporal features, has shown the resonant region widths to extend over about 0.2 to 1.6 L shells for three events detected on the dayside between L = 4 and L = 7. The two events for which plasma density data was available occurred at plasma density gradients in the vicinity of the plasmapause. The standing wave harmonic was determined by the combination of two techniques: the comparison of the observed wave period with that predicted by standing wave theory, and the comparison of the phases of the observed wave electric and magnetic field. The two events analyzed are found to be second harmonic oscillations, suggesting internal generation in the magnetosphere by a bounce resonant mechanism.

Singer, H. J.↗

NASA NTRS1982

A mechanism for plasma waves at the harmonics of the plasma frequency foreshock boundary

A bump-on-tail unstable reduced velocity distribution, constructed from data obtained at the upstream boundary of the electron foreshock by the GSFC electron spectrometer experiment on the ISEE-1 satellite, is used as the initial plasma state for a numerical integration of the 1D-Vlasov-Maxwell system of equations. The integration is carried through the growth of the instability, beyond its saturation, and well into the stabilized plasma regime. A power spectrum computed for the electric field of the stabilized plasma is dominated by a narrow peak at the Bohm-Gross frequency of the unstable field mode but also contains significant power at the harmonics of the Bohm-Gross frequency. The harmonic power is in sharp peaks which are split into closely spaced doublets. The fundamental peak at the Bohm-Gross frequency is split into a closely spaced triplet. The mechanism for excitation of the second harmonic is shown to be second order wave-wave coupling.

Klimas, A. J.↗

NASA NTRS1983

A mechanism for plasma waves at the harmonics of the plasma frequency in the electron foreshock boundary

Klimas, A. J.↗

NASA NTRS1984

Higher harmonic control for rotary wing aircraft

Higher Harmonic Control reduces helicopter airframe vibration through the exercise of rotor blade pitch control at frequencies that are higher harmonics of rotor rotation. Analysis wind tunnel tests and flight tests of this technology with an OH-6A helicopter have led to vibration reduction levels of the order of more than 80 percent. Blade feathering capability at rotor speed harmonics other than the first also promises the improvement of such rotor characteristics as acoustics, aerodynamic efficiency and ground resonance.

Gupta, B. P.↗

NASA NTRS1985

Beam-driven ion cyclotron harmonic resonances in the terrestrial foreshock

A terrestrial upstream wave event which demonstrates multiple, ion cyclotron harmonic resonances between the interplanetary wave population and an observed proton beam is analyzed. The techniques and parameters employed in the data analysis are discussed, including the use of differential and band-pass filters. An upstream wave event demonstrating multiple harmonic waves is examined, and the instability analysis relevant to the ion beam observations thought to be responsible for that event is discussed. It is shown that an observed bi-Maxwellian ion beam is capable of generating right and left-hand polarized waves through ion cyclotron harmonic resonance.

Smith, C. W.↗

NASA NTRS1985

Venus topography - A harmonic analysis

A model of Venusian global topography has been obtained by fitting an eighteenth-degree harmonic series to Pioneer Venus orbiter radar altimeter data. The mean radius is (6051.45 + or - 0.04) km. The corresponding mean density is (5244.8 + or 0.5) kg/cu m. The center of figure is displaced from the center of mass by (0.339 + or - 0.088) km towards (6.6 + or 10.1) deg N, (148. 8 + or - 7.7) deg. The figure of Venus is distinctly triaxial, but the orientation and magnitudes of the principal topographic axes correlate rather poorly with the gravitational principal axes. However, the higher-degree harmonics of topography and gravity are significantly correlated. The topographic variance spectrum of Venus is very similar in form to those of the moon, Mars, and especially earth. It is suggested that this spectral similarity simply reflects a statistical balance between constructional and degradational geomorphic proceses. Venus and earth are particularly similar (and differ from the moon and Mars) in that the larger bodies both exhibit a significant low degree deficit (relative to the extrapolated trend of the higher harmonics).

Bills, B. G.↗

NASA NTRS1985

A preliminary harmonic spline model from Magsat data

A preliminary main field model for 1980 derived from a carefully selected subset of Magsat vector measurements, using the method of harmonic splines, is presented. This model (PHS /80/) for preliminary harmonic splines is the smoothest model (in the sense that the rms radial field at the core surface is minimum) consistent with the measurements (with an rms misfit of 10 nT to account for crustal and external fields as well as noise in the measurement procedure). Therefore PHS (80) is more suitable for studies of the core than models derived with the traditional least squares approach (e.g., GSFC /9/80/). A comparison is conducted of the characteristics of the harmonic spline spectrum, topology of the core field and especially the null-flux curves (loci where the radial field is zero) and the flux through patches bounded by such curves. PHS (80) is less complex than GSFC (9/80) and is therefore more representative of that part of the core field that the data constrain.

Shure, L.↗

NASA NTRS1985

The Type IV burst of 1980 June 29, 0233 UT - Harmonic plasma emission?

Characteristics of the coronal transient which emitted a Type IV radio burst on June 29, 1980 are discussed as to the underlying mechanisms. The Type IV event followed a strong Type II burst which appeared with shock wave. Sources at 80 and 43 MHz were recorded by the radioheliograph on board the SMM satellite. The 80 MHz source moved with the densest part of the transient for a half-hour and was polarized in a manner indicative of harmonic plasma emission, in particular, the second harmonic. The possibility that the 43 MHz signal arose from gyro-synchrotron emission appears unlikely because of the requirement of a 2.8 Gauss magnetic field at 2.5 solar radii. The density of the region emitting the signals was commensurate with calculations of the necessary density for harmonic emission, but too dense for the estimates of the requirements for gyro-synchrotron emissions.

Gary, D. E.↗

NASA NTRS1986

Analysis of the harmonic gyrotron traveling wave amplifier

A single nonlinear differential equation is derived for describing the spatial evolution of the wave field in a gyrotron amplifier on the cylindrical guide geometry. The equation is then used to determine the efficiencies and the optimized interaction lengths for gyrotron operated with TE sub N1 modes at the N-th cyclotron harmonic. The equation offers a significant advantage in simplifying numerical work in comparison with the brute force particle simulation approach. The efficiencies of the harmonic operations by using a hollow beam decrease quickly with increasing harmonic number, but are enhanced by using an axis-encircling beam instead.

Kuo, S. P.↗

NASA NTRS1990

Double-peaked electrostatic ion cyclotron harmonic waves

Electrostatic H(+) cyclotron harmonic waves are often observed along the auroral field lines at altitudes of 1-3.5 R(E) by the Dynamics Explorer 1 satellite. A small fraction of these waves are found to have two peaks associated with each harmonic instead of one peak. The waves occur below the lower hybrid frequency and are usually relatively weak, about a factor of 4 smaller than typical electric field amplitudes of other H(+) cyclotron harmonic wave events. The double-peaked spectral signature is believed to be produced by Doppler shifts arising from the satellite velocity relative to the plasma rest frame. The waves were found to have wavelengths of the order of 300 m and phase velocities of the order of 150 km/s.

Boardsen, S. A.↗