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NASA NTRS1974

The 13th order resonance from Navy tracking on a diademe 2 fragment

A strong constraint on 13th order (odd degree) terms in the geopotential has been derived from Navy tracking on a DIADEME 2 fragment (1967-14F). This object (perigee height: 580 km, orbit inclination: 38.9 deg) is presently decaying slowly through perfect commensurability with these terms. The resonance forces will increase its inclination by 0.02 deg when the passage is complete by late 1974. The constraint (lumped harmonics), derived by adjustment of a pair of harmonic coefficients to the Navy inclination data (principally) is: 10 to the 9th power (14.8 + or - 0.8, 48.3 + or - 0.7) = 0.023(C,S)13,13 -0.172(C,S)15,13 0.505(C,S)17,13 - 0.884(C,S)19,13 + (C,S)21,13 0.673(C,S)23,13 0.099(C,S)25,13 0.295(C,S)27,13 -0.279(C,S)29,13 0.018(C,S)31,13 + There should be a significant contribution to this result from terms as high as 29th degree. But current geopotential solutions (for 13th order terms) to this degree are about 20% in error when judged by this independent data.

Wagner, C. A.↗

NASA NTRS1973

Investigation of the effect of stress on the chemistry, metabolism, and biophysics of collagen

The research is reported concerning the effect of stress on the chemistry in the connective tissue of the rat. It was found that within a day after administration of cortisol (stress harmone), a significant amount of the insoluble collagen disappeared from the skin. It is concluded that the abrupt catabolism of cutaneous collagen releases peptides. These peptides are rapidly degraded to free amino acids which are active in effecting liver glycogen synthesis, and provide a major energy source to assist the animal in the fight or flight reaction. It is proposed that cutaneous collagen represents a reserve energy pool, which can be mobilized via stress harmones.

Houck, J. C.↗

NASA NTRS1974

A theoretical study of the application of jet flap circulation control for reduction of rotor vibratory forces

The results of a study to investigate the theoretical potential of a jet-flap control system for reducing the vertical and horizontal non-cancelling helicopter rotor blade root shears are presented. A computer simulation describing the jet-flap control rotor system was developed to examine the reduction of each harmonic of the transmitted shears as a function of various rotor and jet parameters, rotor operating conditions and rotor configurations. The computer simulation of the air-loads included the influences of nonuniform inflow and blade elastic motions. (no hub motions were allowed.) The rotor trim and total rotor power (including jet compressor power) were also determined. It was found that all harmonics of the transmitted horizontal and vertical shears could be suppressed simultaneously using a single jet control.

Piziali, R. A.↗

NASA NTRS1973

Certain characteristics and capture regions of nonlinear vibrating systems

Free vibrations of a system and vibrations which are multiples of them in frequency are discussed. The corresponding periodic forced vibrations of the type n/m (n is the number of periods of disturbance between periods of movement and m is the number of periods of movement in one period of disturbance), generated by a harmonic or close to harmonic disturbance, are propagated close to the corresponding curves of the free vibrations and their frequency multiples. It has been proposed that investigation of transitional modes of motion and capture regions be carried out by precise methods in phase space, with the least number of coordinates. Thus, for example, for nonautonomous second order equations (for example, the Duffing equations), in place of three variables (coordinates, velocity, phases), it is proposed to use two: velocity during transition of the coordinate through zero and phase.

Ragulskene, V. L.↗

NASA NTRS1973

Electromagnetic radiation trapped in the magnetosphere above the plasma frequency

An electromagnetic noise band is frequently observed in the outer magnetosphere by the Imp 6 spacecraft at frequencies from about 5 to 20 kHz. This noise band generally extends throughout the region from near the plasmapause boundary to near the magnetopause boundary. The noise typically has a broadband field strength of about 5 microvolts/meter. The noise band often has a sharp lower cutoff frequency at about 5 to 10 kHz, and this cutoff has been identified as the local electron plasma frequency. Since the plasma frequency in the plasmasphere and solar wind is usually above 20 kHz, it is concluded that this noise must be trapped in the low-density region between the plasmapause and magnetopause boundaries. The noise bands often contain a harmonic frequency structure which suggests that the radiation is associated with harmonics of the electron cyclotron frequency.

Gurnett, D. A.↗

NASA NTRS1974

A second-order theory of an artificial satellite under the influence of the oblateness of the earth

The general theory of the method of averaging is used to study the effect of the oblateness of the earth on the motion of an artificial satellite. The first-order harmonic J2 and the second-order harmonics J3 and J4 are included in the analysis. The first-order, periodic variations together with the second-order, averaged and secular variations are derived for all the six orbital elements. Alternative orbital elements and necessary relations are introduced to deal with circular orbits, orbits at critical inclination and equatorial orbits. Essential transformations and initialization procedures are also outlined.

Liu, J. J. F.↗

NASA NTRS1974

Effects of curvilinear motion in large-amplitude bending of C3

The geometry of the bending of a linear triatomic molecule is analyzed, and an expression for the average rotational constant is derived. A harmonic oscillator model of C3 is fitted to the observed rotational constant within 0.6%. The bond distance between atoms at zero bending is 1.287 A according to this model; this is noticeably larger than the average internuclear distance of 1.277 A for the vibrational ground state. The first order perturbation solutions for the vibrational energy levels, taking into account the effect of a quartic perturbation potential, closely match observed levels. For a square well potential model of C3, the effect of curvilinear motion in bending is similar to that found for the harmonic oscillator model, though the decreases in energy are about twice as large. In both models, the average energy decrease is relatively constant at approximately 10% over a wide range of vibrational quantum number.

Hansen, C. F.↗

NASA NTRS1974

Stabilization of electron streams in type III solar radio bursts

We show that the electron streams that give rise to type III solar radio bursts are stable and will not be decelerated while propagating out of the solar corona. The stabilization mechanism depends on the parametric oscillating two-stream instability. Radiation is produced near the fundamental and second harmonic of the local electron plasma frequency. Estimates of the emission at the second harmonic indicate that the wave spectra created by the oscillating two-stream instability can account for the observed intensities of type III bursts.

Papadopoulos, K.↗

NASA NTRS1974

Stimulation of the Harris instability in the ionosphere

Observations made with a sweep frequency rf sounder on the satellite ISIS 1 in the topside ionosphere are reported, and the interpretation of diffuse signals at the lower harmonics of the electron cyclotron frequency is discussed. These signals are attributed to the stimulation of Harris instabilities of longitudinal plasma waves at multiples of the cyclotron frequency in a single electron distribution. The Harris instability is excited most readily when the frequency is near the midpoint between the harmonics of the cyclotron frequency. The cause of these instabilities is the large electron velocity anisotropy which results from collisionless cyclotron damping of the energy from the high power sounder pulse.

Benson, R. F.↗

NASA NTRS1975

Laser system with an antiresonant optical ring

Various applications of an antiresonant ring, consisting of a beam splitter and a number of optical reflectors, are described. With a beam splitter having a transmission coefficient and a reflection coefficient, an optical beam incident on the beam splitter along a first axis is split into two components which circulate around the ring in opposite directions. They are recombined to reflect back the beam along the first axis, with none of the beam power being directed along a second axis. The ring can be part of the cavity of two otherwise independent lasers, with two separate laser mediums external to the ring, or with a multi-wavelength laser medium in the ring. The ring together with a second-harmonic generation crystal and a dispersive phase shifter in the ring can generate the second harmonic of an optical beam.

Siegman, A. E.↗

NASA NTRS1975

Gravity fields of the solar system

The most frequently used formulations of the gravitational field are discussed and a standard set of models for the gravity fields of the earth, moon, sun, and other massive bodies in the solar system are defined. The formulas are presented in standard forms, some with instructions for conversion. A point-source or inverse-square model, which represents the external potential of a spherically symmetrical mass distribution by a mathematical point mass without physical dimensions, is considered. An oblate spheroid model is presented, accompanied by an introduction to zonal harmonics. This spheroid model is generalized and forms the basis for a number of the spherical harmonic models which were developed for the earth and moon. The triaxial ellipsoid model is also presented. These models and their application to space missions are discussed.

Zendell, A.↗

NASA NTRS1975

Winter bulge and diurnal variations in hydrogen inferred from AE-C composition measurements

The atomic hydrogen distribution at 250 km during December 1974 solstice was inferred, considering charge exchange equilibrium, from Atmosphere Explorer-C measurements of n(H(+)), n(O(+) and N(O). An empirical model, derived from the observations by least suqare analysis in terms of spherical harmonics, has the following characteristics: (1) n(H) increases by as much as a factor of two between the summer and winter hemispheres, (2) the n(H) diurnal variation is largest at the equator and (3) the diurnal variation is larger in the winter hemisphere than in the summer. Similar analysis of the gas temperature derived from n(N2) measurements reveals that all n(H) and Tg spherical harmonic coefficients are anticorrelated. Both the diurnal and latitudinal (annual) n(H) and Tg amplitudes are in substantial agreement with the zero flux condition, in which exospheric flow dominates the hydrogen distribution. The observed diurnal phase lag of n(H) with respect to Tg is about one hour, agreeing with theory.

Brinton, H. C.↗

NASA NTRS1974

Wind Tunnel Generation of Sinusoidal Lateral and Longitudinal Gusts by Circulation of Twin Parallel Airfoils

A gust generator capable of producing sinusoidal lateral and longitudinal gusts was developed for the purpose of studying the gust response of a model rotor-propeller in a wind tunnel. The gust generator utilized harmonic circulation control of twin parallel airfoils to achieve the harmonic lift variation required for gust generation. The gust generator design, construction, and testing is described. Typical test results are presented in the form of lateral and longitudinal gust perturbation velocities as a function of generator reduced frequency.

Ham, N. D.↗

NASA NTRS1975

Correlation of the earth's rotation rate and the secular change of the geomagnetic field

Power spectral density analysis using Burg's maximum entropy method was applied to the geomagnetic dipole field and its rate of change for the years 1901 to 1969. Both spectra indicate relative maxima at 0.015 cycles/year and its harmonics. These maxima correspond approximately to 66, 33, 22, 17, 13, 11, and 9-year spectral lines. The application of the same analysis techniques to the length-of-day (l.o.d) fluctuations for the period 1865 to 1961 reveal similar spectral characteristics. Although peaks were observed at higher harmonics of the fundamental frequency, the 22-year and 11-year lines are not attributed unambiguously to the solar magnetic cycle and the solar cycle. It is suggested that the similarity in the l.o.d fluctuations and the dipole field variations is related to the motion within the earth's fluid core during the past one hundred years.

Jin, R. S.↗

NASA NTRS1975

Evaluation of geopotential and luni-solar perturbations by a recursive algorithm

The disturbing functions due to the geopotential and Luni-solar attractions are linear and bilinear forms in spherical harmonics. Making use of recurrence relations for the solid spherical harmonics and their derivatives, recurrence formulas are obtained for high degree terms as function of lower degree for any term of those disturbing functions and their derivative with respect to any element. The equations obtained are effective when a numerical integration of the equations of motion is appropriate. In analytical theories, they provide a fast way of obtaining high degree terms starting from initial very simple functions.

Giacaglia, G. E. O.↗

NASA NTRS1975

Analysis of helicopter rotor blade torsional oscillations due to stall

An analysis of stall-induced helicopter rotor blade torsional oscillations was carried out, the primary objectives being to predict the onset and severity of the oscillations and their relationship to aircraft and blade parameters. Blade flapping, flapwise bending, and torsional degrees of freedom were taken into account, with radial variation in aerodynamic loading determined from a previously developed dynamic stall model. Results of analyses were compared with data from flight tests of helicopters. Analyses were carried out while parametrically varying blade vibrational characteristics. It was found that the amplitudes of the higher harmonics of torsional oscillations can be significantly reduced by either reducing the torsional natural frequency or introducing viscous damping in the torsional degree of freedom. A preliminary investigation was conducted to determine the feasibility and practicality of alleviating the stall problem by means of boundary layer control. The results indicate that boundary layer control would be effective in reducing the higher harmonics of torsional oscillations due to stall and that its implementation would not require excessive power or suction rates.

Crimi, P.↗

NASA NTRS1974

On the analytic lunar and solar perturbations of a near earth satellite

The disturbing function of the moon (sun) is expanded as a sum of products of two harmonic functions, one depending on the position of the satellite and the other on the position of the moon (sun). The harmonic functions depending on the position of the perturbing body are developed into trigonometric series with the ecliptic elements l, l prime, F, D and Gamma of the lunar theory which are nearly linear with respect to time. Perturbation of elements are in the form of trigonometric series with the ecliptic lunar elements and the equatorial elements omega and Omega of the satellite, so that analytic integration is simple and the results are accurate over a long period of time.-

Estes, R. H.↗

NASA NTRS1974

Effect of nonsymmetrical flow resistance upon orifice impedance

Previous laboratory work has indicated that an orifice in a thin sheet behaves in a quasisteady manner under acoustical excitation. Also, it has been found that the steady flow resistance of an orifice may be dependent upon the direction of flow, especially in the presence of a crossflow on one side of the hole. An analytical study is presented which assumes a nonreactive orifice in an infinite baffle. The pressure difference across the orifice varies sinusoidally with amplitude 1.0 and average value -P. The orifice resistance is discontinuous at zero velocity and exhibits the constant values when the velocity is nonzero. The resultant velocity has power in all harmonics of the excitation frequency, providing an explanation of the even harmonic excitation observed by other investigators, but not predicted by symmetric nonlinearity. A quasilinear resistance is defined and found to be relatively insensitive to the presence or absence of a resonant backing cavity.

Posey, J. W.↗