Quantum cosmology. I
Hamiltonian methods applied to homogeneous cosmological models, obtaining Einstein equations, passing to quantum theory by imposing canonical commutation relations
Misner, C. W.↗
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Higher order frequency demodulators with feedback
Higher order frequency demodulators with feedback in canonical form and with baseband filter
Hoffman, E.↗
Localized states on a hyperplane
Localized states reconstructed as superposition of canonical states, using hyperplane generalization
Mcdonald, S. C.↗
A hybrid realization for sampled-data controllers
Sampled data compensators hybrid realization for discrete controllers, selecting canonical representation with minimum number of delay elements
Carroll, C. C.↗
A unified treatment of lunar theory and artificial satellite theory
Generalized von Zeipel treatment of lunar and artificial satellite theories, generating single canonical transformation by variable separation technique
Mersman, W. A.↗
Classical adiabatic perturbation theory
Classical Poincare-von Zeipel canonical perturbation theory extension to adiabatically perturbed systems with slow dependence on time or dynamic variables
Stern, D. P.↗
Hamiltonian formulation of guiding center motion
The nonrelativistic guiding center motion of a charged particle in a static magnetic field is derived using the Hamiltonian formalism. By repeated application of first-order canonical perturbation theory, the first two adiabatic invariants and their averaged Hamiltonians are obtained, including the first-order correction terms. Other features of guiding center theory are also given, including lowest order drifts and the flux invariant.
Stern, D. P.↗
Equicontrollability and the model following problem
Equicontrollability and its application to the linear time-invariant model-following problem are discussed. The problem is presented in the form of two systems, the plant and the model. The requirement is to find a controller to apply to the plant so that the resultant compensated plant behaves, in an input-output sense, the same as the model. All systems are assumed to be linear and time-invariant. The basic approach is to find suitable equicontrollable realizations of the plant and model and to utilize feedback so as to produce a controller of minimal state dimension. The concept of equicontrollability is a generalization of control canonical (phase variable) form applied to multivariable systems. It allows one to visualize clearly the effects of feedback and to pinpoint the parameters of a multivariable system which are invariant under feedback. The basic contributions are the development of equicontrollable form; solution of the model-following problem in an entirely algorithmic way, suitable for computer programming; and resolution of questions on system decoupling.
Curran, R. T.↗
Cooling of pulsars
Cooling rates are calculated for superfluid neutron stars of about one solar mass and 10 km radius, with magnetic fields from zero to about 10 to the 14th power Gauss, when possible internal friction effects are neglected. The results show that most old pulsars are so cold that thermal ionization of surface atoms would be negligible. At an age of a million years and with canonical magnetic fields of 10 to the 12th power Gauss, the estimated stellar surface temperature is several thousand to a hundred thousand degrees. However, if we neglect magnetic fields and superfluid states of nucleons, the same surfaces would be about a million degrees.
Tsuruta, S.↗
An improved multiple linear regression and data analysis computer program package
NEWRAP, an improved version of a previous multiple linear regression program called RAPIER, CREDUC, and CRSPLT, allows for a complete regression analysis including cross plots of the independent and dependent variables, correlation coefficients, regression coefficients, analysis of variance tables, t-statistics and their probability levels, rejection of independent variables, plots of residuals against the independent and dependent variables, and a canonical reduction of quadratic response functions useful in optimum seeking experimentation. A major improvement over RAPIER is that all regression calculations are done in double precision arithmetic.
Sidik, S. M.↗
The influence of the great inequality on the secular disturbing function of the planetary system.
This paper derives the contribution by the great inequality to the secular disturbing function of the principal planets. Andoyer's expansion of the planetary disturbing function and von Zeipel's method of eliminating the periodic terms is employed; thereby, the corrected secular disturbing function for the planetary system is derived. The conclusion is drawn that the canonicity of the equations for the secular variation of the heliocentric elements can be preserved if there be retained, in the secular disturbing function, terms only of the second and fourth order relative to the eccentricity and inclinations. The Krylov-Bogoliubov method is suggested for eliminating periodic terms, if it is desired to include the secular perturbations of the fifth and higher order in the heliocentric elements. The additional part of the secular disturbing function derived in this paper can be included in existing theories of the secular effects of principal planets.
Musen, P.↗
Distortion in the frequency demodulator using feedback.
The response of a frequency demodulator using feedback (FMFB) to a frequency modulated signal is analyzed. Canonical equations of operation are obtained. Harmonic distortion is calculated for the case of a sinusoidal modulating signal. Intermodulation distortion is calculated assuming a noise-like modulation. Design curves are presented. The special case of harmonic and intermodulation distortion in a discriminator is also presented. It is shown that the results obtained in this paper by treating the discriminator as a degenerate FMFB compare favorably with those obtained by other authors. However, the results presented here do not require digital computation.
Hoffman, E.↗
Dynamical models for a spacecraft idealized as a set of multi-hinged rigid bodies
A brief description is presented of a canonical set of equations which governs the behavior of an n-body spacecraft. General results are given for the case in which the spacecraft is modeled in terms of n rigid bodies connected by dissipative elastic joints. The final equations are free from constraint torques and involve only r variables (r is the number of degrees of freedom of the system). An advantage which accompanies the elimination of the constraint torques is a decrease in the computer run time (especially when n is large).
Larson, V.↗
Effects of gravity-gradient torque on the rotational motion of a triaxial satellite in a precessing elliptic orbit.
A method of general perturbations, based on the use of Lie series to generate approximate canonical transformations, is applied to study the effects of gravity-gradient torque on the rotational motion of a triaxial, rigid satellite. The center of mass of the satellite is constrained to move in an elliptic orbit about an attracting point mass. The orbit, which has a constant inclination, is free to precess and spin. The method of general perturbations is used to obtain the Hamiltonian for the nonresonant secular and long-period rotational motion of the satellite. The differential equations derivable from the transformed Hamiltonian are integrable, and the solution for the long-term motion may be expressed in terms of Jacobian elliptic functions and elliptic integrals. Geometrical aspects of the long-term rotational motion are discussed, and a comparison of theoretical results with observations is made.
Cochran, J. E.↗
Tree-manipulating systems and Church-Rosser theorems.
Study of a broad class of tree-manipulating systems called subtree replacement systems. The use of this framework is illustrated by general theorems analogous to the Church-Rosser theorem and by applications of these theorems. Sufficient conditions are derived for the Church-Rosser property, and their applications to recursive definitions, the lambda calculus, and parallel programming are discussed. McCarthy's (1963) recursive calculus is extended by allowing a choice between call-by-value and call-by-name. It is shown that recursively defined functions are single-valued despite the nondeterminism of the evaluation algorithm. It is also shown that these functions solve their defining equations in a 'canonical' manner.
Rosen, B. K.↗
The counting recursive digital filter.
Analysis of the bit-level operations involved in the convolutions realizing recursive digital filters leads to hardware designs of such filters based on the operation of counting. Various designs realizing both the canonic and 'direct' forms are presented with particular emphasis on low-cost low-speed high-flexibility machines.
Zohar, S.↗
On the algebraic structure of bilinear systems.
It is shown that a particular bilinear model is both quite general and easy to work with. A basic structure theory is developed with the aid of previous results. Some preliminary ideas are discussed together with the system interconnection, the canonical form, questions of controllability, aspects of observability, and equivalent realizations. It is pointed out that in actually determining equivalent realizations for systems and in the classification of systems, the results available in the study of Lie algebras are of fundamental importance.
Brockett, R. W.↗
Mapping coastal vegetation, land use and environmental impact from ERTS-1
The author has identified the following significant results. Digital analysis of ERTS-1 imagery was used in an attempt to map and inventory the significant ecological communities of Delaware's coastal zone. Eight vegetation and land use discrimination classes were selected: (1) Phragmites communis (giant reed grass); (2) Spartina alterniflora (salt marsh cord grass); (3) Spartina patens (salt marsh hay); (4) shallow water and exposed mud; (5) deep water (greater than 2 m); (6) forest; (7) agriculture; and (8) exposed sand and concrete. Canonical analysis showed the following classification accuracies: Spartina alterniflora, exposed sand, concrete, and forested land - 94% to 100%; shallow water - mud and deep water - 88% and 93% respectively; Phragmites communis 83%; Spartina patens - 52%. Classification accuracy for agriculture was very poor (51%). Limitations of time and available class-memory space resulted in limiting the analysis of agriculture to very gross identification of a class which actually consists of many varied signature classes. Abundant ground truth was available in the form of vegetation maps compiled from color and color infrared photographs. It is believed that with further refinement of training set selection, sufficiently accurate results can be obtained for all categories.
Klemas, V.↗