An approximate method for predicting lunar satellite lifetimes and its application to a lunar orbit mission analysis.
Approximate method for predicting lunar satellite lifetimes and application to lunar orbit mission analysis
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Approximate method for predicting lunar satellite lifetimes and application to lunar orbit mission analysis
Combination into unified setting of various results for approximate solution of fixed point equation, using iterative process
Approximate method for predicting lunar satellite lifetimes and application to lunar orbit mission analysis
Finite dimensional approximations of optimal nonlinear filters for class of large-noise, nonlinear, continuous-time problems
Algorithm for construction of discrete approximations to linear differential expressions in terms of ordinates
Time optimal feedback control using extension of Hermes approximation theorem
Approximate method for electric propulsion missions analysis, determining system components effects on performance
This paper describes rover safety issues and presents an approximate reasoning approach to maintaining vehicle safety in a navigational context.
The effective-medium approximation (EMA) is based on the assumption that a heterogeneous particle can have a homogeneous counterpart possessing similar scattering and absorption properties. We analyze the numerical accuracy of the EMA by comparing superposition T-matrix computations for spherical aerosol particles filled with numerous randomly distributed small inclusions and Lorenz-Mie computations based on the Maxwell-Garnett mixing rule. We verify numerically that the EMA can indeed be realized for inclusion size parameters smaller than a threshold value. The threshold size parameter depends on the refractive-index contrast between the host and inclusion materials and quite often does not exceed several tenths, especially in calculations of the scattering matrix and the absorption cross section. As the inclusion size parameter approaches the threshold value, the scattering-matrix errors of the EMA start to grow with increasing the host size parameter and or the number of inclusions. We confirm, in particular, the existence of the effective-medium regime in the important case of dust aerosols with hematite or air-bubble inclusions, but then the large refractive-index contrast necessitates inclusion size parameters of the order of a few tenths. Irrespective of the highly restricted conditions of applicability of the EMA, our results provide further evidence that the effective-medium regime must be a direct corollary of the macroscopic Maxwell equations under specific assumptions.
The Community Radiative Transfer Model (CRTM) is a fast model that requires bulk optical properties of hydrometeors in the form of lookup tables to simulate all-sky satellite radiances. Current cloud scattering lookup tables of CRTM were generated using the Mie-Lorenz theory thus assuming spherical shapes for all frozen habits, while actual clouds contain frozen hydrometeors with different shapes. The Discrete Dipole Approximation (DDA) technique is an effective technique for simulating the optical properties of non-spherical hydrometeors in the microwave region. This paper discusses the implementation and validation of a comprehensive DDA cloud scattering database into CRTM for the microwave frequencies. The original DDA database assumes total random orientation in the calculation of single scattering properties. The mass scattering parameters required by CRTM were then computed from single scattering properties and water content dependent particle size distributions. The new lookup tables eliminate the requirement for providing the effective radius as input to CRTM by using the cloud water content for the mass dimension. A collocated dataset of short-term forecasts from Integrated Forecast System of the European Centre for Medium-Range Weather Forecasts and satellite microwave data was used for the evaluation of results. The results overall showed that the DDA lookup tables, in comparison with the Mie tables, greatly reduce the differences among simulated and observed values. The Mie lookup tables especially introduce excessive scattering for the channels operating below 90 GHz and low scattering for the channels above 90 GHz.
Formulation and digital coding of approximate hydrogen properties for application to flow computations
Hypersonic approximation of the minimum semiapex angle giving subsonic flow behind an attached shock
Approximations to wiener optimum filters and predictors
Comparison of exact and approximate solutions for nonequilibrium nozzle flows
Correction to second approximation calculation of geomagnetic field, solar wind interface
Approximate solution to nonlinear differential equation of third order with bogolyubov asymptotic method
Adaptive state vector control - section 7, approximations to state vector control
A method for approximating the vacuum motions of spinning rigid symmetrical bodies with varying spin rates and inertias has been completed. The analysis includes the effects of time varying thrust misalignments, mass unbalance, and jet damping. Results are given in the form of equations for space referenced Euler angles, flight-path angles, body referenced attitude rates, and earth-referenced vehicle-trajectory coordinates. The method consists of dividing the problem into intervals during which the time-dependent variables are assumed constant at their mean interval value. In order to check this procedure, solutions for various interval sizes are compared with solutions obtained with numerical methods. Although the method is somewhat lengthy for accurate hand computation in most cases, it is readily programed for machine solutions. Probably more important, the general solutions give insight into the separate effects of the variables and, in many cases, can be quickly used to determine the approximate ranges of the variables required for the desired solution to a given problem. In this respect, equations for determining maximum wobble have been derived for certain input conditions. The method has been shown to compare closely with the numerical solutions of two sample problems. The sample problems also illustrated the relatively large effect of pitch and yaw jet damping on body motions.