Triaxial antenna Patent
Pattern and impedance matching improvements in transversely polarized triaxial antenna
Black, W. W.↗
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Certain comments on the application of the method of averaging to the study of the rotational motions of a triaxial rigid body
Averaging technique applied to variational equations describing rotational motions of rigid triaxial body in elliptical orbit
Liu, J. J. F.↗
Further comments on the application of the method of averaging to the study of the rotational motions of a triaxial rigid body, part 2
The second and final step in the development of first-order secular solutions to rotational motions of triaxial bodies is presented.
Liu, J. J. F.↗
Further comments on the application of the method of averaging to the study of the rotational motions of a triaxial rigid body, part 3
Variational equations were applied to the case of a rapidly spinning triaxial body moving in an elliptic orbit, in which the orbital plane is regressing at a constant rate. The explicit differential equations obtained in this application were integrated by the method of averaging to develop secular analytical expressions, which, to first-order in a small parameter, describe the complete space motions of the rigid body under the influence of nonresonant gravity-gradient perturbations. The effects of aerodynamic torque on the rotational motion of an orbiting satellite are studied, as another example of the application of the variational equations derived and the method of averaging.
Liu, J. J. F.↗
Effects of gravity-gradient torque on the rotational motion of a triaxial satellite in a precessing elliptic orbit.
A method of general perturbations, based on the use of Lie series to generate approximate canonical transformations, is applied to study the effects of gravity-gradient torque on the rotational motion of a triaxial, rigid satellite. The center of mass of the satellite is constrained to move in an elliptic orbit about an attracting point mass. The orbit, which has a constant inclination, is free to precess and spin. The method of general perturbations is used to obtain the Hamiltonian for the nonresonant secular and long-period rotational motion of the satellite. The differential equations derivable from the transformed Hamiltonian are integrable, and the solution for the long-term motion may be expressed in terms of Jacobian elliptic functions and elliptic integrals. Geometrical aspects of the long-term rotational motion are discussed, and a comparison of theoretical results with observations is made.
Cochran, J. E.↗
Poisson equations of rotational motion for a rigid triaxial body with application to a tumbling artificial satellite
A mathematical model is developed for studying the effects of gravity gradient torque on the attitude stability of a tumbling triaxial rigid satellite. Poisson equations are used to investigate the rotation of the satellite (which is in elliptical orbit about an attracting point mass) about its center of mass. An averaging method is employed to obtain an intermediate set of differential equations for the nonresonant, secular behavior of the osculating elements which describe the rotational motions of the satellite, and the averaged equations are then integrated to obtain long-term secular solutions for the osculating elements.
Liu, J. J. F.↗
Vector magnetometer design study: Analysis of a triaxial fluxgate sensor design demonstrates that all MAGSAT Vector Magnetometer specifications can be met
The design of the vector magnetometer selected for analysis is capable of exceeding the required accuracy of 5 gamma per vector field component. The principal elements that assure this performance level are very low power dissipation triaxial feedback coils surrounding ring core flux-gates and temperature control of the critical components of two-loop feedback electronics. An analysis of the calibration problem points to the need for improved test facilities.
Adams, D. F.↗
Triaxial digital fluxgate magnetometer for NASA applications explorer mission: Results of tests of critical elements
Tests performed to prove the critical elements of the triaxial digital fluxgate magnetometer design were described. A method for improving the linearity of the analog to digital converter portion of the instrument was studied in detail. A sawtooth waveform was added to the signal being measured before the A/D conversion, and averaging the digital readings over one cycle of the sawtooth. It was intended to reduce bit error nonlinearities present in the A/D converter which could be expected to be as much as 16 gamma if not reduced. No such nonlinearities were detected in the output of the instrument which included the feature designed to reduce these nonlinearities. However, a small scale nonlinearity of plus or minus 2 gamma with a 64 gamma repetition rate was observed in the unit tested. A design improvement intended to eliminate this small scale nonlinearity was examined.
Mcleod, M. G.↗
Radar backscattering from a rough rotating triaxial ellipsoid with applications to the geodesy of small asteroids
Radar geodesy of the asteroid 433 Eros was reported by Jurgens and Goldstein (1976). Their measurements were based on the spectral properties of a rough rotating triaxial ellipsoid. This paper presents the theory by which theoretical spectra based on a backscattering model of the form of the nth power of the cosine of theta, or any reasonable backscattering model, can be computed. Some general properties of these spectra are demonstrated, and simple measurements of the apparent radar cross section, center frequency, and effective bandwidth as a function of time are shown to be useful in determining the sizes of the semi-major axes, the exponent n in the scattering model, the backscatter efficiency of the surface material, the rotation period, and the declination of the observer above or below the rotation equator. Some of these parameters are correlated, and multiple estimation may be difficult unless the observations span a period sufficiently long so as to present a wide range of declinations of the observer. However, the departure from a spherical shape aids in separating the scattering properties from the target dimensions and facilitates the simultaneous estimation of all free parameters.
Jurgens, R. F.↗
On the stability of Schwarzschild's triaxial galaxy model
The numerical model for a triaxial galaxy constructed by Schwartzschild (1979) has been tested by means of fully self-consistent three-dimensional n-body numerical experiments that use a representation of this model to start the integration. The integration, study models, initial load, and correcting potential of the experiment are detailed. Preliminary checks included density values, potential values, and integration in potential of an ideal model. The results showed some particle loss and no significant shape change. The model is rugged and robust, and no growing disturbances with growth rate in excess of 0.5 per crossing time could be detected. Runs were done at 50 percent excess halo and with tube orbits reversed.
Smith, B. F.↗
Internal stresses in Phobos and other triaxial bodies
The unusual dynamical behavior of Phobos, its strange appearance, and its mysterious network of grooves all make it an intriguing object. Geophysical studies, though, have been hampered by the lack of suitable theories applicable to nonspherical bodies. In this paper the Martian satellites are modeled as homogeneous, elastic triaxial ellipsoids subject to tidal, rotational, and self-gravitational stresses. A novel semianalytical treatment then gives the stress and strain fields throughout their interiors. Yield phenomena and their possible surface expressions are also investigated. The results indicate that Phobos and Deimos have always been stable with respect to tidal fracture or disruption, but that Phobos will probably break up before colliding with Mars. Applications of the new formulation to other nonspherical bodies in the solar system are also discussed.
Dobrovolskis, A. R.↗
Miniature triaxial metastable ionization detector for gas chromatographic trace analysis of extraterrestrial volatiles
The present investigation is concerned with a miniature metastable ionization detector featuring an unconventional electrode configuration, whose performance characteristics parallel those of traditional design. The ionization detector is to be incorporated in a flight gas chromatograph (GC) for use in the Space Shuttle. The design of the detector is discussed, taking into account studies which verified the sensitivity of the detector. The triaxial design of the detector is compared with a flat-plate style. The obtained results show that the principal goal of developing a miniature, highly sensitive ionization detector for flight applications was achieved. Improved fabrication techniques will utilize glass-to-metal seals and brazing procedures.
Woeller, F. H.↗
A phoenics model for the triaxial loading of an initially cylindrical mass of rate-type material with provisions for bulging and yield
This work traces the response of a granular material via the Ten Coefficient Truesdell rate-type constituitive model into the simplest meaningful loading: the triaxial test configuration. A functional relation has been posed for computing the rather peculiar relation between average applied stress and average porosity. Using that relation an attack has been mounted on the dilemma that exists between dynamic and constitutive use of the pressure variable; that is relating dynamic pressure, thermodynamic pressure, stress deviator and higher stress invariants. The resolution was as a linear superposition with a one-way feedback, in that while the dynamic component could not effect the constituitive component, the converse was not true since density appears in the momentum transport relation.
French, K. W., Jr.↗
Geodetic altitude to a triaxial ellipsoidal planet
An efficient theoretical model for determining geodetic altitudes with better than millimeter accuracy is proposed, with application to the TOPEX/Poseidon project. The triaxial ellipsoidal subsurface point of a satellite is used as the initial trial solution to achieve an efficient and simple iterative solution. It is found that the second-iteration solution is exact to an accuracy of at least 10 to the -9th km.
Tang, Charles C. H.↗
A highly triaxial N-body system tumbling about is intermediate axis
The results are presented of an N-body simulation which shows that it is possible for a highly triaxial self-gravitating system in dynamical equilibrium to exhibit stable figure rotation about its intermediate axis. The system is long-lived, lasting at least 20 half-mass crossing times of the final system. The nature of the simulation is summarized.
Duncan, Martin J.↗
Triaxial ellipsoid dimensions and rotational pole of 2 Pallas from two stellar occultations
The ability to derive unique triaxial ellipsoid dimensions and a rotational pole for an asteroid is demonstrated on the basis of three stellar occultations. Two such occultations for Pallas are used to examine the locus of solutions falling along a curve in seven-dimensional parameter space. While the first occultation slightly overestimated the true size of the asteroid's outline, more plausible solutions are allowed within its errors. The occultation model is combined with speckle interferometric results. Pallas is more flattened, with a greater b/c ratio, and smaller c, than found in previous estimates.
Drummond, Jack D.↗
The effect of galaxy triaxiality on globular clusters
Evidence of triaxiality and central mass concentration in the Galaxy and in M31 and M87 is examined. It is proposed that globular clusters on box orbits in the inner parts of these systems pass close enough to the center to be destroyed by tidal shocks. Remaining clusters will preferentially populate tube orbits with relatively high angular momentum. The process is used to explain the cluster distribution in M87 reported by Lauer and Kormendy (1986). Models are presented for cluster destruction by massive black holes in M87's dark halo. Consideration is given to techniques for testing the suggestion that clusters form only on box orbits.
Ostriker, J. P.↗
Orbital decay in aspherical galaxies. II - Triaxial systems
A previous analysis of orbital decay of small satellite galaxies into moderately oblate, axisymmetrical cannibal galaxies with Staeckel potentials is generalized here to triaxial systems with arbitary anisotropy and internal streaming. The orbital evolution to be expected in systems with differing degrees of anisotropy or rotation is briefly discussed. The evolution of some representative orbits is presented in detail using the orbit-averaged anisotropic Chandrasekhar drag and the distribution functions for perfect ellipsoids. The validity of orbit averaging is assessed by comparing the results with ensembles of single-particle orbits integrated directly in the same potential and the same drag prescription. An attempt is made to gauge the validity of the Chandrasekhar formula by comparison with restricted N-body solutions. It is found that the orbit-averaged evolution is consistent with such simulations.
Statler, Thomas S.↗