Partial wave theory of H sub 2 - Calculation of sigma sub g super plus states.
Partial wave theory of two electron diatomic hydrogen molecules and calculation in zeroth order for sigma g states
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Partial wave theory of two electron diatomic hydrogen molecules and calculation in zeroth order for sigma g states
In the early days of spaceflight, the gBig Sky h theory was the near universally accepted paradigm for dealing with collisions of orbiting objects. This theory was also used during the early years of the aviation industry. Just as it did in aviation, the gBig Sky h theory breaks down as more and more objects accumulate in the environment. Fortunately, by the late 1970 fs some visionaries in NASA and the US Department of Defense (DoD) realized that trends in the orbital environment would inevitably lead to increased risks to operational spacecraft from collisions with other orbiting objects. The NASA Orbital Debris Program was established at and has been conducted at Johnson Space Center since 1979. At the start of 1979, fewer than 5000 objects were being tracked by the US Space Surveillance Network and very few attempts had been made to sample the environment for smaller sizes. Today, the number of tracked objects has quadrupled. Ground ]based and in situ measurements have statistically sampled the LEO environment over most sizes and mitigation guidelines and requirements are common among most space faring nations. NASA has been a leader, not only in defining the debris environment, but in promoting awareness of the issues in the US and internationally, and in providing leadership in developing policies to address the issue. This paper will discuss in broad terms the evolution of the NASA debris program from its beginnings to its present broad range of debris related research. The paper will discuss in some detail current research topics and will attempt to predict future research trends.
In this paper, step-by-step procedures of applying the H-infinity theory to robust control systems design are given. The objective of the paper is to eliminate the possible difficulties a control engineer may encounter in applying H-infinity control theory and to clear up some misconceptions about H-infinity theory like high-gain controller and numerical obstacles, etc. An efficient algorithm is used to compute the optimal H-infinity norm. The Glover and Doyle (1988) controller formulas are slightly modified and used to construct an optimal controller without any numerical difficulties.
The applicability of H infinity control theory to the problems of large space structures (LSS) control was investigated. A complete evaluation to any technique as a candidate for large space structure control involves analytical evaluation, algorithmic evaluation, evaluation via simulation studies, and experimental evaluation. The results of analytical and algorithmic evaluations are documented. The analytical evaluation involves the determination of the appropriateness of the underlying assumptions inherent in the H infinity theory, the determination of the capability of the H infinity theory to achieve the design goals likely to be imposed on an LSS control design, and the identification of any LSS specific simplifications or complications of the theory. The resuls of the analytical evaluation are presented in the form of a tutorial on the subject of H infinity control theory with the LSS control designer in mind. The algorthmic evaluation of H infinity for LSS control pertains to the identification of general, high level algorithms for effecting the application of H infinity to LSS control problems, the identification of specific, numerically reliable algorithms necessary for a computer implementation of the general algorithms, the recommendation of a flexible software system for implementing the H infinity design steps, and ultimately the actual development of the necessary computer codes. Finally, the state of the art in H infinity applications is summarized with a brief outline of the most promising areas of current research.
H beta, H gamma and H delta Stark broadened profiles, investigating perturbing electron- radiating atom inelastic collisions, Gaunt factors and half widths
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Thirty years of control systems research has produced an enormous body of theoretical results in feedback synthesis. Yet such results see relatively little practical application, and there remains an unsettling gap between classical single-loop techniques (Nyquist, Bode, root locus, pole placement) and modern multivariable approaches (LQG and H infinity theory). Large scale, complex systems, such as high performance aircraft and flexible space structures, now demand efficient, reliable design of multivariable feedback controllers which optimally tradeoff performance against modeling accuracy, bandwidth, sensor noise, actuator power, and control law complexity. A methodology is described which encompasses numerous practical design constraints within a single unified formulation. The approach, which is based upon coupled systems or modified Riccati and Lyapunov equations, encompasses time-domain linear-quadratic-Gaussian theory and frequency-domain H theory, as well as classical objectives such as gain and phase margin via the Nyquist circle criterion. In addition, this approach encompasses the optimal projection approach to reduced-order controller design. The current status of the overall theory will be reviewed including both continuous-time and discrete-time (sampled-data) formulations.
Resonance theory of thermomolecular recombination kinetics applied to hydrogen atoms
Resonance theory of thermolecular atomic recombination kinetics based on transition complexes identification as quasi-bound states or orbiting resonances
Equations for estimating orbit prediction accuracy theory, with partial derivatives calculated from two-body elliptical orbit theory
Intensity of radiation transfer in Doppler broadened resonance line expressed in terms of appropriate H-functions assuming semi-infinite atmosphere
RESONCE THEORY OF TERMOLECULAR RECOMBINATION kinetics
Space science - step rocket optimization theory
The applicability of the complex-potential theory to H(-)-He collisions is investigated. Measurements are conducted of the elastic differential cross section for H(-)-He collisions, taking into account energies in the range from 5 to 120 eV. A preliminary determination is made of the energy spectrum of detached electrons. The results are interpreted in terms of the complex-potential theory. The crossing point is determined together with the general shape of the HeH(-) potential curve.
During this research period we have made significant progress in the four proposed areas: (1) design of robust controllers via H infinity optimization; (2) design of robust controllers via mixed H2/H infinity optimization; (3) M-delta structure and robust stability analysis for structured uncertainties; and (4) a study on controllability and observability of perturbed plant. It is well known now that the two-Riccati-equation solution to the H infinity control problem can be used to characterize all possible stabilizing optimal or suboptimal H infinity controllers if the optimal H infinity norm or gamma, an upper bound of a suboptimal H infinity norm, is given. In this research, we discovered some useful properties of these H infinity Riccati solutions. Among them, the most prominent one is that the spectral radius of the product of these two Riccati solutions is a continuous, nonincreasing, convex function of gamma in the domain of interest. Based on these properties, quadratically convergent algorithms are developed to compute the optimal H infinity norm. We also set up a detailed procedure for applying the H infinity theory to robust control systems design. The desire to design controllers with H infinity robustness but H(exp 2) performance has recently resulted in mixed H(exp 2) and H infinity control problem formulation. The mixed H(exp 2)/H infinity problem have drawn the attention of many investigators. However, solution is only available for special cases of this problem. We formulated a relatively realistic control problem with H(exp 2) performance index and H infinity robustness constraint into a more general mixed H(exp 2)/H infinity problem. No optimal solution yet is available for this more general mixed H(exp 2)/H infinity problem. Although the optimal solution for this mixed H(exp 2)/H infinity control has not yet been found, we proposed a design approach which can be used through proper choice of the available design parameters to influence both robustness and performance. For a large class of linear time-invariant systems with real parametric perturbations, the coefficient vector of the characteristic polynomial is a multilinear function of the real parameter vector. Based on this multilinear mapping relationship together with the recent developments for polytopic polynomials and parameter domain partition technique, we proposed an iterative algorithm for coupling the real structured singular value.
Five analytical tools have been used to study rotor performance at high advance ratio. One is representative of autogyro rotor theory in 1934 and four are representative of helicopter rotor theory in 2008. The five theories are measured against three sets of well documented, full-scale, isolated rotor performance experiments. The major finding of this study is that the decades spent by many rotorcraft theoreticians to improve prediction of basic rotor aerodynamic performance has paid off. This payoff, illustrated by comparing the CAMRAD II comprehensive code and Wheatley & Bailey theory to H-34 test data, shows that rational rotor lift to drag ratios are now predictable. The 1934 theory predicted L/D ratios as high as 15. CAMRAD II predictions compared well with H-34 test data having L/D ratios more on the order of 7 to 9. However, the detailed examination of the selected codes compared to H-34 test data indicates that not one of the codes can predict to engineering accuracy above an advance ratio of 0.62 the control positions and shaft angle of attack required for a given lift. There is no full-scale rotor performance data available for advance ratios above 1.0 and extrapolation of currently available data to advance ratios on the order of 2.0 is unreasonable despite the needs of future rotorcraft. Therefore, it is recommended that an overly strong full-scale rotor blade set be obtained and tested in a suitable wind tunnel to at least an advance ratio of 2.5. A tail rotor from a Sikorsky CH-53 or other large single rotor helicopter should be adequate for this exploratory experiment.
Exchange perturbation theories applied to delta function model of molecular hydrogen ion, discussing EL-HAV second order energy at large internuclear separations
Seven QSOs of low to intermediate redshift are characterized on the basis of: 320-850-nm spectra obtained with the UVITS spectrograph and image-dissector scanner at the f/9 Cassegrain focus of the 2.7-m reflecting telescope at McDonald Observatory; improved model calculations for the Fe II, Mg II, and Balmer lines and the Balmer continuum; and the theoretical results of Netzer and Wills (1983). The data are presented in tables, spectra, and difference spectra and described in detail. Fe II is found to be the largest contributor to the emission line spectrum, with strong UV Fe II lines in all QSOs (regardless of the strength of the optical Fe II lines) and an abundance ratio suggesting a factor-of-three overabundance of Fe relative to Mg and probably H. A discrepancy between the observed Fe II strength and the predictions of dustless standard photoionization models is noted, and the addition of a high-density component to the models is suggested.