Modified long-period behavior due to tesseral harmonics.
Von Zeipel method and Hamiltonian perturbation mechanics used for orbits at resonance with tesseral harmonics of geopotential
Vagners, J.↗
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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Polarizability of molecular hydrogen.
Perturbation theory summation method for calculating molecular hydrogen static dipole electric polarizability, using coupled Hartree- Fock approximation
Taylor, H. S.↗
Optimal three dimensional reentry trajectories for Apollo-type vehicles
Numerical optimization method based on perturbation theory for calculating optimal three dimensional reentry trajectories for Apollo type vehicles
Williamson, W. E., Jr.↗
Velocity of the solar wind as determined from interplanetary scintillations.
The method of smooth perturbations is used to derive the equations for interplanetary scintillation in a (statistically) spherically symmetric solar wind with constant wind velocity. The expressions, valid in the limit of small scintillation index, are used to discuss the relation between the radial wind velocity and the observed projected velocity of the scintillation pattern. It is found that the pattern velocity is systematically less than the wind velocity by a substantial fraction, depending on the radial variation of the density fluctuations. If the fluctuations fall off as 1/r-squared the correction is 18 percent, whereas if the fluctuations are proportional to 1/r the correction is 57 percent. The effects may be even more severe if the solar wind is not spherically symmetric.
Jokipii, J. R.↗
Thermodynamic properties of gases dissolved in electrolyte solutions.
A method based on perturbation theory for mixtures is applied to the prediction of thermodynamic properties of gases dissolved in electrolyte solutions. The theory is compared with experimental data for the dependence of the solute activity coefficient on concentration, temperature, and pressure; calculations are included for partial molal enthalpy and volume of the dissolved gas. The theory is also compared with previous theories for salt effects and found to be superior. The calculations are best for salting-out systems. The qualitative feature of salting-in is predicted by the theory, but quantitative predictions are not satisfactory for such systems; this is attributed to approximations made in evaluating the perturbation terms.
Tiepel, E. W.↗
A note on velocity-related series expansions in the two-body problem
The present note describes a few important series expansions in the two-body problem. They are related to the magnitude v of the velocity vector and are important for the treatment of atmospheric drag by the method of general perturbations. These series have been obtained with computerized Poisson series manipulations. The results are given to order seven in the eccentricity, for both the mean anomaly and the true anomaly.
Broucke, R.↗
The motion of a satellite in resonance with the longitude-dependent harmonics
The solution to the motion of a satellite in an eccentric orbit and in resonance with one or more of the longitude-dependent harmonics of the central planet is developed. The method of solution parallels the well known von Zeipel method of general perturbations. The solution consists of expressions for the variations of the Delaunay variables. These expressions are composed of the perturbations developed by Brouwer in 1959 for the motion of an artificial satellite plus first-order resonant perturbations due to longitude-dependent harmonics (in terms of Legendre normal elliptic integrals of the first and second kind).
Dallas, S. S.↗
Multifrequency techniques for studying interplanetary scintillations
Rytov's approximation, or the method of smooth perturbations, is utilized to derive the temporal frequency spectra of the amplitude and phase fluctuations of multifrequency plane and spherical waves propagating in the interplanetary medium and solar corona. It is shown that multifrequency observations of interplanetary scintillations using either compact radio stars of spacecraft radio signals are desirable because the correlation of the multifrequency waves yields additional independent measurements of the solar wind and turbulence. Measurements of phase fluctuations are also desirable because, unlike amplitude fluctuations, they provide information on the full range of scale sizes for the electron-density fluctuations. It is also shown that a coherent dual-frequency radio system is particularly useful in making such measurements. In addition to providing a means for interpreting observations of multifrequency interplanetary scintillations, the present analysis is essential for estimating the effects of solar corona turbulence on the communications and navigation of a spacecraft whose line-of-sight path passes close to the sun.
Woo, R.↗
The motion of a satellite in resonance with the longitude-dependent harmonics
The solution to the motion of a satellite in an eccentric orbit and in resonance with one or more of the longitude-dependent harmonics of the central planet is developed. The method of solution parallels the well known von Zeipel method of general perturbations. The solution consists of expressions for the variations of the Delaunay variables. These expressions are composed of the perturbations developed by Brouwer in 1959 for the motion of an artificial satellite plus first-order resonant perturbations due to longitude-dependent harmonics (in terms of Legendre normal elliptic integrals of the first and second kind).
Dallas, S. S.↗
The motion of a satellite in resonance with the second-degree sectorial harmonic
The solution to the motion of a satellite in an eccentric orbit and in resonance with the second-degree sectorial harmonic of the potential field is developed. The method of solution used parallels the well known von Zeipel method of general perturbations. The solution consists of expressions for the variations of the Delaunay variables. These expressions are composed of the perturbations developed by Brouwer in 1959 for the motion of an artificial satellite plus first-order perturbations due to the second-degree sectorial harmonic (in terms of the Legendre normal elliptic integrals of the first and second kind).
Dallas, S. S.↗
Electrostatic disturbance forces on a 3-axis drag-free sensor
The electrostatic analysis of a multiple-capacitance 3-axis drag-free sensor is presented in this paper. The instrument consists of a proof-mass (a dense metallic ball) floating freely inside a spherical cavity enclosed by the sensor plates and the shield. Since the ball and the cavity are not necessarily concentric, the problem in three-dimensional potential theory for electrostatics is solved by the method of boundary perturbations and specifically in terms of spherical harmonics. The capacitance outputs of the instrument and the electrostatic forces acting on the system are derived as non-linear functions of the ball position, ball charge and the sensor plate potentials. The instrument sensitivity and cross-coupling effects are discussed. The analysis may also be useful for electrostatic gyros and suspensions.
Hagstrom, T.↗
Effect of limb darkening functions variations on deconvolution of wide-field-of-view measurements of earth emitted radiation
A solution is presented to the problem of deconvolving wide field of view measurements of earth-emitted radiation for the case of limb-darkening functions which are geographically dependent. The method of linear perturbations is used and the effects of limb-darkening function variations at various scales are evaluated. A simple model for the geographical variation of the limb-darkening function based on the radiant exitance is introduced. It is shown that the effect of these variations on the global average radiant exitance vanishes identically, and is insignificant for large spatial scales. For wave numbers six through twelve, the limb-darkening effects are small but possibly significant. At wave numbers greater than twelve, the noise due to meteorological variability dominates for an orbit altitude of 1100 km. The smallness of these effects is due to the smoothness of the monthly averaged radiant exitance field.
Smith, G. L.↗
A Numerical Method of Calculating Propeller Noise Including Acoustic Nonlinear Effects
Using the transonic flow fields(s) generated by the NASPROP-E computer code for an eight blade SR3-series propeller, a theoretical method is investigated to calculate the total noise values and frequency content in the acoustic near and far field without using the Ffowcs Williams - Hawkings equation. The flow field is numerically generated using an implicit three dimensional Euler equation solver in weak conservation law form. Numerical damping is required by the differencing method for stability in three dimensions, and the influence of the damping on the calculated acoustic values is investigated. The acoustic near field is solved by integrating with respect to time the pressure oscillations induced at a stationary observer location. The acoustic far field is calculated from the near field primitive variables as generated by NASPROP-E computer code using a method involving a perturbation velocity potential as suggested by Hawkings in the calculation of the acoustic pressure time-history at a specified far field observed location. the methodologies described are valid for calculating total noise levels and are applicable to any propeller geometry for which a flow field solution is available.
Korkan, K. D.↗
A simple microgravity table for the Orbiter or Space Station
Methods of limiting perturbations in microgravity experiments are proposed. An acceleration level below 10 to the -4th m/s-squared is necessary to maintain an undisturbed microgravity environment. Machinery vibrations, crew motion, and the firing of vernier thrusters produce acceleration levels greate than 10 to the -4th m/s-squared. The use of a weak spring system or simple electromagnets to isolate an experimental table from these factors is described. The manners in which crew motion and vernier firing are countered by the springs are examined. The steady acceleration caused by atmospheric drag, gravity gradient force, and steady rotation can be maintained below 10 to the -th m/s-squared; however, the springs can protect the table from these accelerations if required.
Garriott, O. K.↗
Transonic viscous flow calculations for a turbine cascade with a two equation turbulence model
A numerical method for the study of steady, transonic, turbulent viscous flow through plane turbine cascades is presented. The governing equations are written in Favre-averaged form and closed with a first order model. The turbulent quantities are expressed according to a two-equation kappa-epsilon model where low Reynolds number and compressibility effects are included. The solution is obtained by using a pseudo-unsteady method with improved perturbation propagation properties. The equations are discretized in space by using a finite volume formulation. An explicit multistage dissipative Runge-Kutta algorithm is then used to advance the flow equations in the pseudo-time. First results of calculations compare fairly well with experimental data.
Boretti, A. A.↗
Hyperfine magnetic field on Cd-111 in Heusler alloys Co2MnZ (Z = Si, Ga, Ge, Sn)
The time differential perturbed angular correlation method has been used to measure, as a function of temperature, the hyperfine magnetic field at Cd sites in the Heusler alloys Co2MnZ (Z = Si, Ga, Ge, Sn). The hyperfine fields, normalized to the total magnetic moment per formula unit, show an approximately linear trend toward more positive values with increasing lattice parameter.
Jha, S.↗
SCISEAL: A CFD code for analysis of fluid dynamic forces in seals
A viewgraph presentation is made of the objectives, capabilities, and test results of the computer code SCISEAL. Currently, the seal code has: a finite volume, pressure-based integration scheme; colocated variables with strong conservation approach; high-order spatial differencing, up to third-order; up to second-order temporal differencing; a comprehensive set of boundary conditions; a variety of turbulence models and surface roughness treatment; moving grid formulation for arbitrary rotor whirl; rotor dynamic coefficients calculated by the circular whirl and numerical shaker methods; and small perturbation capabilities to handle centered and eccentric seals.
Athavale, Mahesh↗
Modeling, Modal Properties, and Mesh Stiffness Variation Instabilities of Planetary Gears
Planetary gear noise and vibration are primary concerns in their applications in helicopters, automobiles, aircraft engines, heavy machinery and marine vehicles. Dynamic analysis is essential to the noise and vibration reduction. This work analytically investigates some critical issues and advances the understanding of planetary gear dynamics. A lumped-parameter model is built for the dynamic analysis of general planetary gears. The unique properties of the natural frequency spectra and vibration modes are rigorously characterized. These special structures apply for general planetary gears with cyclic symmetry and, in practically important case, systems with diametrically opposed planets. The special vibration properties are useful for subsequent research. Taking advantage of the derived modal properties, the natural frequency and vibration mode sensitivities to design parameters are investigated. The key parameters include mesh stiffnesses, support/bearing stiffnesses, component masses, moments of inertia, and operating speed. The eigen-sensitivities are expressed in simple, closed-form formulae associated with modal strain and kinetic energies. As disorders (e.g., mesh stiffness variation. manufacturing and assembling errors) disturb the cyclic symmetry of planetary gears, their effects on the free vibration properties are quantitatively examined. Well-defined veering rules are derived to identify dramatic changes of natural frequencies and vibration modes under parameter variations. The knowledge of free vibration properties, eigen-sensitivities, and veering rules provide important information to effectively tune the natural frequencies and optimize structural design to minimize noise and vibration. Parametric instabilities excited by mesh stiffness variations are analytically studied for multi-mesh gear systems. The discrepancies of previous studies on parametric instability of two-stage gear chains are clarified using perturbation and numerical methods. The operating conditions causing parametric instabilities are expressed in closed-form suitable for design guidance. Using the well-defined modal properties of planetary gears, the effects of mesh parameters on parametric instability are analytically identified. Simple formulae are obtained to suppress particular instabilities by adjusting contact ratios and mesh phasing.
Parker, Robert G.↗