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Full CI calculations have been performed on the CH3 radical. The full CI results are compared to those obtained using CASSCF/multireference CI and coupled-pair functional methods, both at the equilibrium CH distance and at geometries with the three CH bonds extended. In general, the performance of the approximate methods is similar to that observed in calculations on other molecules in which one or two bonds were stretched.
A new aproach to the solution of determination of surface principal curvatures and directions is proposed. Direct relationships between the principal curvatures and directions of the tool surface and those of the principal curvatures and directions of generated gear surface are obtained. The principal curvatures and directions of geartooth surface are obtained without using the complicated equations of these surfaces. A general theory of the train kinematical errors exerted by manufacturing and assembly errors is discussed. Two methods for the determination of the train kinematical errors can be worked out: (1) with aid of a computer, and (2) with a approximate method. Results from noise and vibration measurement conducted on a helicopter transmission are used to illustrate the principals contained in the theory of kinematic errors.
The detailed mission and system optimization of low thrust electric propulsion missions is a complex, iterative process involving interaction between orbital mechanics and system performance. Through the use of appropriate approximations, initial system optimization and analysis can be performed for a range of missions. The intent of these calculations is to provide system and mission designers with simple methods to assess system design without requiring access or detailed knowledge of numerical calculus of variations optimizations codes and methods. Approximations for the mission/system optimization of Earth orbital transfer and Mars mission have been derived. Analyses include the variation of thruster efficiency with specific impulse. Optimum specific impulse, payload fraction, and power/payload ratios are calculated. The accuracy of these methods is tested and found to be reasonable for initial scoping studies. Results of optimization for Space Exploration Initiative lunar cargo and Mars missions are presented for a range of power system and thruster options.
A reliable method is presented for calculating the flowfield about a cascade of arbitrary 2-D airfoils. The method approximates the three-dimensional flow in a turbomachinery blade row by correcting for streamtube convergence and radius change in the throughflow direction. The method is a fully conservative solution of the full potential equation incorporating the finite volume technique on a body-fitted periodic mesh, with an artificial density imposed in the transonic region to ensure stability and the capture of shock waves. Comparison of results for several supercritical blades shows good agreement with their hodograph solutions. Other calculations for these profiles as well as standard NACA blade sections indicate that this is a useful scheme for analyzing both the design and off-design performance of turbomachinery blading.
This paper presents some exact solutions of problems in random function theory for the purpose of testing the validity of an approximate method known variously in the many different fields of its application as first order smoothing theory, first order cumulant discard, quasilinear theory, or the adiabatic approximation. The hydromagnetic dynamo equations are used here, as particularly appropriate for such an investigation. The calculations show that in one case the exact and approximate solutions agree. In the other case the approximate solution is wrong. Hence, in the absence of a general criterion for validity, a result based on first order smoothing theory is a conjecture rather than a fact. This impacts strongly on much of the recent work on hydromagnetic dynamos.
This paper presents an approximate method for obtaining truncated balance realizations of systems represented by non-rational transfer functions, that is infinite dimensional systems. It is based on the approximation to the Hankel operator.
A methodology employed in engineering codes to predict aerodynamic characteristics over arbitrary supersonic/hypersonic configurations is considered. Engineering codes use a combination of simplified methods, based on geometrical impact angle and freestream conditions, to compute pressure distribution over the vehicle's surface in an efficient and timely manner. These approximate methods are valid for both hypersonic (Mach greater than 4) and lower speeds (Mach down to 2). It is concluded that the proposed methodology enables the user to obtain reasonable estimates of vehicle performance and engineering methods are valuable in the design process of these type of vehicles.
In this paper, an on-line control approach which will adjust the steady-state shape of a large antenna arbitarily close to any achievable desired profile is proposed. The method makes use of distributed parameter system theory and allows refocusing using a limited number of control actuators and sensors. The controller gains are calculated by approximating the solution to an infinite-dimensional optimal quasi-static control problem. A very general convergence result for such quasi-static controllers is proved and applied to the antenna controller to show convergence, using any Galerkin (finite-element) approximation method.
Full CI calculations are presented for the 1A1, 3B1, and 1B1 states of SiH2 at their respective equilibrium geometries and at geometries with the SiH bonds stretched. These results are compared with those obtained from single-reference and multireference CI calculations. The computed Te values agree well with the full CI results, provided that the effects of higher-than-double excitations are accounted for either by the Davidson correction or by a multireference approach. When the SiH bonds are stretched, the single-reference methods are not sufficiently flexible, and only CASSCF/MRCI achieves chemical accuracy (i.e., agrees with the full CI to 1 kcal/mol). Overall, the accuracy of the various approximate methods is very similar to that found for H2O, NH2, and CH2.
Texture analysis would permit improved autonomous, onboard science data interpretation for adaptive navigation, sampling, and downlink decisions. These analyses would assist with terrain analysis and instrument placement in both macroscopic and microscopic image data products. Unfortunately, most state-of-the-art texture analysis demands computationally expensive convolutions of filters involving many floating-point operations. This makes them infeasible for radiation- hardened computers and spaceflight hardware. A new method approximates traditional texture classification of each image pixel with a fast decision-tree classifier. The classifier uses image features derived from simple filtering operations involving integer arithmetic. The texture analysis method is therefore amenable to implementation on FPGA (field-programmable gate array) hardware. Image features based on the "integral image" transform produce descriptive and efficient texture descriptors. Training the decision tree on a set of training data yields a classification scheme that produces reasonable approximations of optimal "texton" analysis at a fraction of the computational cost. A decision-tree learning algorithm employing the traditional k-means criterion of inter-cluster variance is used to learn tree structure from training data. The result is an efficient and accurate summary of surface morphology in images. This work is an evolutionary advance that unites several previous algorithms (k-means clustering, integral images, decision trees) and applies them to a new problem domain (morphology analysis for autonomous science during remote exploration). Advantages include order-of-magnitude improvements in runtime, feasibility for FPGA hardware, and significant improvements in texture classification accuracy.
It is often important to perform sensitivity analysis to determine how a structural model will be impacted by design changes. Often, the structural analysts will manually make changes to the finite element model (FEM) to determine the effects. But when dealing with a large FEM with millions of degrees of freedom these manual changes can be cumbersome and calculation of the effects can computationally expensive. Therefore, it is desirable to determine the effects of model changes through approximation methods. One common technique is to determine the analytical sensitivity of the FEM model with respect to the given change. These analytical sensitivities are valid when small changes are made to the structural model, but invalid if large changes need to be assessed. Another approach is to use Structural Dynamic Modification (SDM) to create a surrogate model to analyze model changes. SDM is a widely-used sensitivity method and is used in applications of model updating, uncertainty quantification, and model design studies. SMD is valid for moderate (10-20 percent) changes in the structural model, but model approximations are often needed for large parameter changes (greater than 20 percent). Structural Dynamic Modification can be improved by using residual vectors to augment the surrogate model formulation from SDM. Adding the residual modes increases the fidelity of the surrogate model while keeping the computational cost low. This paper discusses the application and limitations of the augmented residual modes method to two structures: the Integrated Spacecraft and Payload Element (ISPE) of the Space Launch System (SLS) and the full SLS as it is configured during its Integrated Modal Test (IMT).
The ability to simulate camera line of sight and field of view is a powerful capability for flight mechanics simulations. This paper improves upon an existing camera visibility implementation that leverages geometry to estimate parachute visibility from a singular point by introducing a shape discretization method. The new method approximates a shape as a set of analytical points relative to a target marker within any number of camera fields of view. The method is developed in such a way to be generalized to a myriad of spacecraft applications. This effort focuses on an implementation to simulate parachute canopy visibility within the combined field of view of three cameras but additional applications are discussed. Monte Carlo analysis is used to assess the parachute canopy visibility example and demonstrate its improved performance over the previous method.
The ability to simulate camera line of sight and field of view is a powerful capability for flight mechanics simulations. This paper improves upon an existing camera visibility implementation that leverages geometry to estimate parachute visibility from a singular point by introducing a shape discretization method. The new method approximates a shape as a set of analytical points relative to a target marker within any number of camera fields of view. The method is developed in such a way to be generalized to a myriad of spacecraft applications. This effort focuses on an implementation to simulate parachute canopy visibility within the combined field of view of three cameras but additional applications are discussed. Monte Carlo analysis is used to assess the parachute canopy visibility example and demonstrate its improved performance over the previous method.
This NASA grant supported the development of codes to solve the non-LTE multi-level spherical radiative transfer problem in the presence of velocity fields. Much of this work was done in collaboration with Graham Harper (CASA, University of Colorado). These codes were developed for application to the cool, low-velocity winds of evolved late-type stars. Particular emphasis was placed on modeling the wind of lambda Velorum (K4 lb), the brightest K supergiant in the sky, based on extensive observations of the ultraviolet spectrum with the HST/GHRS from GO program 5307. Several solution techniques were examined, including the Eddington factor Approach described in detail by Bennett & Harper (1997). An Eddington factor variant of Harper's S-MULTI code (Harper 1994) for stationary atmospheres was developed and implemented, although full convergence was not realized. The ratio of wind terminal velocity to turbulent velocity is large (approx. 0.3-0.5) in these cool star winds so this assumption of stationarity provides reasonable starting models. Final models, incorporating specified wind laws, were converged using the comoving CRD S-MULTI code. Details of the solution procedure were published by Bennett & Harper (1997). Our analysis of the wind of lambda Vel, based on wind absorption superimposed on chromospheric emission lines in the ultraviolet, can be found in Carpenter et al. (1999). In this paper, we compare observed wind absorption features to an exact CRD calculation in the comoving frame, and also to a much quicker, but approximate, method using the SEI (Sobolev with Exact Integration) code of Lamers, Cerruti-Sola, & Perinotto (1987). Carpenter et al. (1999) provide detailed comparisons of the exact CRD and approximate SEI results and discuss when SEI is adequate to use for computing wind line profiles. Unfortunately, the observational material is insufficient to unambiguously determine the wind acceleration law for lambda Vel. Relatively few unblended Fe II lines of optical depth sensitive to the wind acceleration region are present in the existing HST/GHRS data set. Most of the Fe II lines are either too optically thick (resulting in a board, black wind absorption profile) or too optically thin (resulting in no wind absorption feature present). Also, most of the ultraviolet spectra obtained from HST GO-5307 was at medium resolution (R approx. 40,000, corresponding to a velocity resolution of 7.5 km/s). This is simply inadequate to resolve the turbulence in the outer wind; a key parameter in theoretical wind models. We can now say that an unambiguous determination of the wind velocity law in lambda Vel will require complete coverage of the ultraviolet spectrum at high dispersion (R approx. 10(exp 5), or 3 km/s). This is now feasible usin, the STIS echelle spectrograph on-board HST.
A method of economically evaluating the hydrodynamic forces generated in a gas-lubricated tilting-pad bearing is presented. The numerical method consists of solving the case of the infinite width bearing and then converting this solution to the case of the finite bearing by accounting for end leakage. The approximate method is compared to the finite-difference solution of Reynolds equation and yields acceptable accuracy while running about one-hundred times faster. A mathematical model of a gas-lubricated tilting-pad vertical rotor systems is developed. The model is capable of analyzing a two-bearing-rotor system in which the rotor center of mass is not at midspan by accounting for gyroscopic moments. The numerical results from the model are compared to actual test data as well as analytical results of other investigators.
This paper reviews existing techniques for calculating dynamic loads for flexible airplanes and presents a new technique. The new technique involves the summation-of-forces method of writing dynamic loads equations. Until now this form of the dynamic loads equations has been formulated in the frequency domain. The new technique uses s-plane approximation methods (previously applied only to the equations of motion) to transform the dynamic loads equations from a second-order frequency-domain formulation with frequency-dependent coefficients into a linear-time-invariant state-space formulation. Several numerical examples demonstrate the usefulfness of the new technique and the high quality of the results. In addition, a convergence investigation establishes that the summation-of-forces method converges more quickly (that is, with fewer modes) than does the mode displacement method.
A method of solution is presented, which, when applied to the elasto-plastic analysis of plates having a v-notch on one edge and subjected to pure bending, will produce stress and strain fields in much greater detail than presently available. Application of the boundary integral equation method results in two coupled Fredholm-type integral equations, subject to prescribed boundary conditions. These equations are replaced by a system of simultaneous algebraic equations and solved by a successive approximation method employing Prandtl-Reuss incremental plasticity relations. The method is first applied to number of elasto-static problems and the results compared with available solutions. Good agreement is obtained in all cases. The elasto-plastic analysis provides detailed stress and strain distributions for several cases of plates with various notch angles and notch depths. A strain hardening material is assumed and both plane strain and plane stress conditions are considered.
An optimal Routh approximant of a single-input single-output dynamic system is a reduced-order transfer function of which the denominator is obtained by the Routh approximation method while the numerator is determined by minimizing a time-response integral-squared-error (ISE) criterion. In this paper, a new elegant approach is presented for obtaining the optimal Routh approximants for linear time-invariant continuous-time systems. The approach is based on the Routh canonical expansion, which is a finite-term orthogonal series of rational basis functions, and minimization of the ISE criterion. A procedure for combining the above approach with the bilinear transformation is also presented in order to obtain the optimal bilinear Routh approximants of linear time-invariant discrete-time systems. The proposed technique is simple in formulation and is amenable to practical implementation.