Ionization of excited atomic hydrogen by electron collision.
Coulomb Born approximation derived for ionization of hydrogen atom by electron collision when atom is in any given initial state
IONIZATION CROSS SECTION↗
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Results for “initial state”
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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A new algorithm for a class of quadratic programming problems with application to control.
New algorithm for quadratic programming problems with application to control, determining input requiring minimum time from initial state to target state
SAMPLED DATA SYSTEM↗
A computational technique for the design of a specific optimal controller.
Parametric input/output relation of approximate controller with optimized performance index, obtaining specific optimal control designed in regard to worst initial state
OPTIMAL CONTROL↗
Collisionally induced photoabsorption by the H/-/ ion
Charged particle interaction influence on photoionization cross section of negative hydrogen ion, considering initial state polarization leading to free s wave electron
Watson, W. D.↗
Reachable sets for linear dynamical systems.
The properties of reachable sets for linear dynamical systems for specified control sets are discussed. Iterative procedures for determining numerical approximations of the reachable set are suggested and methods of obtaining an admissible control function which transfers an initial state to as near a prescribed target as possible is described. The problem of reachability with multiple control constraints is discussed and certain aspects of reachability for time-invariant systems with adjustable parameters is considered.
Pecsvaradi, T.↗
Discontinuities and shock waves in the interplanetary medium and their interaction with the magnetosphere.
The discontinuous structure of the solar wind is described with emphasis on properties related to geomagnetic impulses. Some of the discontinuities are clearly hydromagnetic shocks and tangential discontinuities, and can produce a significant change in the momentum flux at the magnetosphere boundary. Such a change generates an impulse which propagates through the magnetosphere to the earth where it is observed world-wide as an impulse in magnetograms. The propagation process is not reviewed here, but the relation between the initial cause (discontinuity) and the final effect (geomagnetic impulse) is reviewed in detail. The various types of impulses are examined, and are related qualitatively to the various types of discontinuities. The magnitude of an impulse is related to the change in the momentum flux. The propagation time and the rise time depend on the propagation process rather than on the initial state.
Burlaga, L. F.↗
Further comparison of theory and experiment for decay of homogeneous turbulence.
An analysis of the decay of homogeneous turbulence from a given initial state is compared with the experiment of Lin and Huang (1970). Comparisons were made for decay of turbulent energy, decay of energy-transfer spectra, decay of three-dimensional turbulent-energy spectra, and decay of higher-order spectral quantities V, R, and S, where these respectively represent functionals of three-, four-, and five-point spectral quantities. Good agreement between theory and experiment is noted.
Deissler, R. G.↗
Origin and early development of the planets.
Extensive numerical calculations have been carried out to determine the structure of the primitive solar nebula. The resulting structure shows a dominance of the radial pressure gradient near the center, and a dominance of the centrifugal forces throughout most of the outer region. Thermal convection and Eddington-Sweet circulation currents can be expected to cause a rapid dissipation of the disk, requiring only a few centuries. It is therefore postulated that the planets were formed in an exceedingly hot initial state due to their rapid rates of accumulation. Beyond one or two astronomical units from the center, the original interstellar grains should not be completely destroyed during the formation of the disk, and these will form the nuclei for subsequent chemical condensations and chemical accumulation. Inside this distance, nucleation of condensed materials must occur within the nebular gases.
Cameron, A. G. W.↗
N-burn optimal analytic trajectories.
Derivation of N-burn analytic solutions for propellant-optimal transfer trajectories of a vehicle in a vacuum between arbitrary boundary conditions. Variational changes in the desired boundary conditions are expressed, in general, in terms of variational changes in the control vector and in the initial state vector. All coefficient matrices are computed recursively in terms of the analytic matrices established from the subarcs of the N-burn solution. The solution is applicable to shuttle ascent (exoatmospheric), rendezvous, and deorbit problems. Consideration is also given to state-variable and control-variable inequality constraints.
Jezewski, D. J.↗
Computation of optimal output-feedback compensators for linear time-invariant systems
The control of linear time-invariant systems with respect to a quadratic performance criterion was considered, subject to the constraint that the control vector be a constant linear transformation of the output vector. The optimal feedback matrix, f*, was selected to optimize the expected performance, given the covariance of the initial state. It is first shown that the expected performance criterion can be expressed as the ratio of two multinomials in the element of f. This expression provides the basis for a feasible method of determining f* in the case of single-input single-output systems. A number of iterative algorithms are then proposed for the calculation of f* for multiple input-output systems. For two of these, monotone convergence is proved, but they involve the solution of nonlinear matrix equations at each iteration. Another is proposed involving the solution of Lyapunov equations at each iteration, and the gradual increase of the magnitude of a penalty function. Experience with this algorithm will be needed to determine whether or not it does, indeed, possess desirable convergence properties, and whether it can be used to determine the globally optimal f*.
Platzman, L. K.↗
Differential games.
General discussion of the theory of differential games with two players and zero sum. Games starting at a fixed initial state and ending at a fixed final time are analyzed. Strategies for the games are defined. The existence of saddle values and saddle points is considered. A stochastic version of a differential game is used to examine the synthesis problem.
Varaiya, P. P.↗
Classification, scale series and nomenclature of lunar charts
Lunar charts are classified with an eye toward solution of special problems of lunar cartography. The initial state of mapping the moon will require charts with scales of 1:5,000,000; 1:1,000,000; 1:250,000; 1:50,000; and 1:10,000.
Florenskiy, K. P.↗
Multiplet effects on the L(2,3) fluorescence yield of multiply ionized Ar
The 2p fluorescence yield of argon in the presence of 0 to 6 3p holes was calculated by statistically averaging the fluorescence yields of initial state that consist of individual multiplet configurations. These configurations were formed by coupling the 2p vacancy to the partially filled 3p shell. Results agree reasonably well with experimental fluorescence yields deduced from ion-atom collision measurements.
Chen, M. H.↗
Discrete optimal control approach to a four-dimensional guidance problem near terminal areas
Description of a computer-oriented technique to generate the necessary control inputs to guide an aircraft in a given time from a given initial state to a prescribed final state subject to the constraints on airspeed, acceleration, and pitch and bank angles of the aircraft. A discrete-time mathematical model requiring five state variables and three control variables is obtained, assuming steady wind and zero sideslip. The guidance problem is posed as a discrete nonlinear optimal control problem with a cost functional of Bolza form. A solution technique for the control problem is investigated, and numerical examples are presented. It is believed that this approach should prove to be useful in automated air traffic control schemes near large terminal areas.
Nagarajan, N.↗
Curved descending landing approach guidance and control
Linear optimal regulator theory is applied to a nonlinear simulation of a transport aircraft performing a helical landing approach. A closed form expression for the quasi-steady nominal flight path is presented along with the method for determining the corresponding constant nominal control inputs. The Jacobian matrices and the weighting matrices in the cost functional are time varying. A method of solving for the optimal feedback gains is reviewed. The control system is tested on several alternative landing approaches using both three and six degree flight path angles. On each landing approach, the aircraft was subjected to large random initial state errors and to randomly directed crosswinds. The system was also tested for sensitivity to changes in the parameters of the aircraft and of the atmosphere. Performance of the optimal controller on all the three degree approaches was very good, and the control system proved to be reasonably insensitive to parametric uncertainties.
Crawford, D. J.↗
Automatic guidance and control of a transport aircraft during a helical landing approach
A linear optimal regulator theory was applied to a nonlinear simulation of a transport aircraft performing a helical landing approach. A closed-form expression for the quasi-steady nominal flight path is presented along with the method for determining the corresponding constant nominal control inputs. The Jacobian matrices and the weighting matrices in the cost functional were time varying. A method of solving for the optimal feedback gains is reviewed. The control system was tested on several alternative landing approaches using both 3 deg and 6 deg flight path angles. On each landing approach, the aircraft was subjected to large random initial-state errors and to randomly directed crosswinds. The system was also tested for sensitivity to changes in the parameters of the aircraft and of the atmosphere. Results indicate that performance of the optimal controller on all the 3 deg approaches is very good. The control system proved to be reasonably insensitive to parametric uncertainties. Performance is not as good on the 6 deg approaches. A modification to the 6 deg flight path was proposed for the purpose of improving performance.
Crawford, D. J.↗
Calculations of the early evolution of Jupiter
The evolution of the protoplanet Jupiter is followed, using a hydrodynamic computer code with radiative energy transport. Jupiter is assumed to have formed as a subcondensation in the primitive solar nebula at a density just high enough for gravitational collapse to occur. The initial state has a density of 0.0015 nanograms per cu cm and a temperature of 43 K; the calculations are carried to an equilibrium state where the central density reaches 0.5 g per cu cm and the central temperature reaches 25,000 K. During the early part of the evolution the object contracts in quasi-hydrostatic equilibrium; later on hydrodynamic collapse occurs, induced by the dissociation of hydrogen molecules. After dissociation is complete, the planet regains hydrostatic equilibrium with a radius of a few times the present value. Further evolution beyond this point is not treated here; however the results are consistent with the existence of a high-luminosity phase shortly after the planet settles into its final quasi-static contraction.-
Bodenheimer, P.↗
Multiplet effects on the L/sub 2,3/ fluorescence yield of multiply ionized Ar
The 2p fluorescence yield of Ar in the presence of zero to six 3p holes has been calculated by statistically averaging the fluorescence yields of initial states that consist of individual multiplet configurations, formed by coupling the 2p vacancy to the partially filled 3p shell. The L(sub 2,3) fluorescence yields for the (2p)-1 (3p)-n configurations of Ar are found to be 1.48, 17.97, 24.83, 37.84, 79.61, 112.16, and 121.48 x .0001 for n = 0, 1, 2, 3, 4, 5, and 6, respectively. Results agree reasonably well with experimental fluorescence yields deduced from ion-atom collision measurements.
Chen, M. H.↗