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Proposal of an algorithmic procedure, based on mathematical programming methods, to design compensators for hyperstable discrete model-reference adaptive systems (MRAS). The objective of the compensator is to render the MRAS insensitive to initial parameter estimates within a maximized hypercube in the model parameter space.
A study is made of the mathematical solution of the differential equation of motion of a test particle in the equatorial plane of the Kerr gravitational field, using S (Schwarzschild-like) coordinates. A qualitative solution of this equation leads to the conclusion that there can only be 25 different types of orbits. For each value of a, the results are presented in a master diagram for which h and e are the parameters. A master diagram divides the h, e parameter space into regions such that at each point within one of these regions the types of admissible orbits are qualitatively the same. A pictorial representation of the physical orbits in the r, phi plane is also given.
The work to advance the state-of-the-art of miminum distance classification is reportd. This is accomplished through a combination of theoretical and comprehensive experimental investigations based on multispectral scanner data. A survey of the literature for suitable distance measures was conducted and the results of this survey are presented. It is shown that minimum distance classification, using density estimators and Kullback-Leibler numbers as the distance measure, is equivalent to a form of maximum likelihood sample classification. It is also shown that for the parametric case, minimum distance classification is equivalent to nearest neighbor classification in the parameter space.
The attitude stability of a class of spinning flexible spacecraft in a force-free environment is analyzed. The spacecraft is modeled as a rigid core having attached to it a flexible appendage idealized as a collection of elastically interconnected particles. Liapunov stability theorems are employed with the Hamiltonian of the system, constrained through the angular momentum integral so as to admit complete damping, used as a testing function. The Hamiltonian is written in terms of modal coordinates as interpreted by the hybrid coordinate formulation, thus allowing truncation to a level amenable to literal stability analysis. Testing functions are constructed for a spacecraft with an arbitrary (discretized) appendage, and closed form stability criteria are generated for the first mode of a restricted appendage model lying in a plane which contains the center of mass and is orthogonal to the spin axis. The criteria are (except for idealized cases on the stability boundary line in the parameter space) both necessary and sufficient for stability for any spacecraft characterized by the planar appendage model, such as a spacecraft containing solar panels and/or radial booms.
Ridge, Marquardt's generalized inverse, shrunken, and principal components estimators are discussed in terms of the objectives of point estimation of parameters, estimation of the predictive regression function, and hypothesis testing. It is found that as the normal equations approach singularity, more consideration must be given to estimable functions of the parameters as opposed to estimation of the full parameter vector; that biased estimators all introduce constraints on the parameter space; that adoption of mean squared error as a criterion of goodness should be independent of the degree of singularity; and that ordinary least-squares subset regression is the best overall method.
The subsonic doublet-lattice method (DLM) aeroelastic analysis in NASTRAN was successfully applied to produce subsonic flutter boundary data in parameter space for a large delta wing configuration. Computed flow velocity and flutter frequency values as functions of air density ratio, flow Mach number, and reduced frequency are tabulated. The relevance and the meaning of the calculated results are discussed. Several input-deck problems encountered and overcome are cited with the hope that they may be helpful to NASTRAN Rigid Format 45 users.
Results are reported for observations of solar 584-A flux resonantly scattered by the 1s(2)-1s2p transition of neutral interstellar helium. A photometer equipped with a helium gas-absorption cell and flown aboard a sounding rocket to a peak altitude of 185 km was employed to observe the sky in Perseus. The data reduction procedure is described, including subtraction of the terrestrial atmospheric background, calculation of the solar flux, and reduction of the number density of scatters to a function of phase-space parameters of the local interstellar medium. The ratio of 584-A fluxes observed with the gas cell full and empty is computed and compared with numerical models of the interstellar-helium flow through the solar system. The results show that the bulk speed of the distant interstellar medium with respect to the sun is unlikely to be less than 10 to 15 km/s, at the 2-sigma level. Since this value is inconsistent with results obtained from Lyman-alpha observations, it is suggested that either the total ionization rate for helium is variable or present models of the behavior of the local interstellar medium need further refinement.
The first and second variations are calculated for the irreducible form of Hamilton's Principle that involves the minimum number of dependent variables necessary to describe the kinetmatics and thermodynamics of inviscid, compressible, baroclinic flow in a specified gravitational field. The form of the second variation shows that, in the neighborhood of a stationary point that corresponds to physically stable flow, the action integral is a complex saddle surface in parameter space. There exists a form of Hamilton's Principle for which a direct solution of a flow problem is possible. This second form is related to the first by a Friedrichs transformation of the thermodynamic variables. This introduces an extra dependent variable, but the first and second variations are shown to have direct physical significance, namely they are equal to the free energy of fluctuations about the equilibrium flow that satisfies the equations of motion. If this equilibrium flow is physically stable, and if a very weak second order integral constraint on the correlation between the fluctuations of otherwise independent variables is satisfied, then the second variation of the action integral for this free energy form of Hamilton's Principle is positive-definite, so the action integral is a minimum, and can serve as the basis for a direct trail and error solution. The second order integral constraint states that the unavailable energy must be maximum at equilibrium, i.e. the fluctuations must be so correlated as to produce a second order decrease in the total unavailable energy.
Design refinement is described for baseline F-8C adaptive flight test control laws which consist of simplified quadratic-optimal model-following control structures in the pitch and lateral directional axes. The variable gains of both axes are adjusted adaptively by an explicit on-line maximum likelihood parameter identifier. The identifier, consisting of five parallel computing channels which evaluate the likelihood functions at discrete points in parameter space, operates in pitch only, using pitch rate, normal acceleration, and elevator position measurements.
An explicit adaptive control algorithm based on maximum likelihood estimation of parameters has been designed for NASA's DFBW F-8 aircraft. To avoid iterative calculations, the algorithm uses parallel channels of Kalman filters operating at fixed locations in parameter space. This algorithm has been implemented in NASA/DFRC's Remotely Augmented Vehicle (RAV) facility. Real-time sensor outputs (rate gyro, accelerometer and surface position) are telemetered to a ground computer which sends new gain values to an on-board system. Ground test data and flight records were used to establish design values of noise statistics and to verify the ground-based adaptive software. The software and its performance evaluation based on flight data are described
Flow visualization studies and laser Doppler anemometer measurements on swirling water flows reveal six distinct types of very large amplitude disturbance modes of the vortex core. Three, 'axisymmetric' and spiral vortex breakdowns, and the 'double helix,' have been described by others. A definite order of evolution in parameter space (Reynolds number and circulations) occurs, and is described. Puzzling responses of the axisymmetric and spiral vortex breakdowns to imposed flow transients reported previously are confirmed here, and are traced to the shedding of starting and stopping vortices from swirl vanes. Conclusions bearing upon the validity of some theories of vortex breakdown are possible from the data.
The reported investigation constitutes an extension of studies conducted by Ashour-Abdalla and Kennel (1975, 1976, 1978) with respect to a basic plasma model of Young et al. (1973). The model involves a combination of a cold Maxwellian background plasma, a hot plasma, and a 'loss cone' type of free energy source. Previous results on the first cyclotron harmonic bands are extended to multiharmonics. The significance of the obtained relations is discussed and tentative conclusions are presented. Given that the spatial growth rates of the convective modes are comparable, and that simultaneous nonconvective instability (NCI) is possible, it is concluded that multiharmonic emissions ought to be a common feature of the magnetospheric electrostatic wave observations. Since the volume of parameter space for which the first harmonic is NCI, and the volume for which the convective first harmonic mode has significant spatial growth rates, exceed those for the higher harmonics, first harmonic waves should be the most commonly observed and the higher harmonics should usually be accompanied by the first harmonic.
Alternating direction implicit (ADI) schemes for two-dimensional parabolic equations with a mixed derivative are constructed by using the class of all A sub 0-stable linear two-step methods in conjunction with the method of approximation factorization. The mixed derivative is treated with an explicit two-step method which is compatible with an implicit A sub 0-stable method. The parameter space for which the resulting ADI schemes are second order accurate and unconditionally stable is determined. Some numerical examples are given.
The dispersion relation for small amplitude waves in a hot relativistic plasma embedded in a uniform magnetic field is derived. Four plasma modes exist for propagation oblique to the magnetic field, and the mode properties are summarized in a hot relativistic generalization of the cold plasma pond diagram of Stix (1962). The two-fluid approximation is considered, and two-fluid equations are applied in this procedure which summarizes properties of linear waves in an unbounded magnetized relativistic plasma by means of a parameter-space diagram of wave phase velocity.
It is noted that thermally driven flows in rotating laboratory containers with cylindrical geometry can be axially symmetric or wavelike depending on the experimental parameters. In anticipation that rotating fluid experiments might soon be done in spherical shell geometry, Barcilon's model has been extended to a beta-plane channel in order to gain a rough understanding of the effects of rotating spherical geometry. An incompressible fluid version of the Charney (1947) model of baroclinic instability, modified to include Ekman pumping at rigid horizontal boundaries is used. With this model, stability boundaries are mapped out for individual zonal wavenumbers in the parameter space used by Barcilon.
The SETI (Search for Extraterrestrial Intelligence) Project's primary thrust is to search the microwave region of the spectrum for signals of extraterrestrial intelligent origin. The project will search a well defined volume of search parameter space using existing antennae and a sophisticated data acquisition and analysis system. Two major components are included, the target survey, which will observe at very high sensitivity all attractive stellar candidates within 75 light years of the Sun, and the sky survey, which will observe the entire celestial sphere at a lower sensitivity.
Collisions of spherical galaxies were studied in a series of numerical experiments to see what happens when galaxies collide. Each experiment starts with two model galaxies, each consisting of 50,000 stars, moving toward each other along a specified orbit. The series of experiments provides a systematic sampling of the parameter space spanned by the initial orbital energy and the initial angular momentum. Deeply penetrating collisions are emphasized. The collisions reported here scale to relative velocities as great as 500 km/s, well into the range for collisions within clusters of galaxies. It is found that: (1) the galaxies contract momentarily to about half their original sizes shortly after close passage; and (2) the initial galaxies blend into a single dynamical system while they are near each other.
An analytical solution is presented for the baroclinic stability problem of a Boussinesq fluid in a beta-plane channel with Ekman suction boundary conditions. All of the modes, stable and unstable, belonging to this problem are identified. It is found that an unstable mode exists for only a certain range of values of the Burger number. The value of the Burger number at the upper limit of this range increases as the Ekman number decreases. Beyond this upper limit only a damped mode exists. It is also found that this transition in parameter space from the unstable to the stable mode occurs in a discontinuous manner.