Scalar-tensor theory in canonical form. I
Scalar-tensor theory in canonical form, discussing neutral particle and electron self energy problem
Toton, E. T.↗
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A new formulation of canonical perturbation theory
Canonical perturbation theory formulation applied to Poincare-von Zeipel method
Stern, D. P.↗
Linear and regular celestial mechanics- Perturbed two-body motion, numerical methods, canonical theory
Book on linear and ordinary celestial mechanics covering perturbed two body motion, numerical methods, canonical theory and initial value problems
Scheifele, G.↗
The canonization of nice variables
Kruskal transformation canonization of perturbed periodic systems with Hamiltonian
Stern, D. P.↗
Classification of ERTS-1 MSS data by canonical analysis
Classification of ERTS-1 MSS data by canonical analysis
Lachowski, H. M.↗
Analytical satellite theories based on a new set of canonical elements
A new analytical satellite theory is presented. Instead of the 6 classical elements of Delaunay, a set of 8 canonical elements is used. Whereas the time is the independent variable in classical theory, the true anomaly is the independent variable in the new theory. The new approach has four features: (1) The amount of formulas in the solution is reduced considerably. (2) The first order results are almost as accurate as second order results in classical theory. (3) The theory is easier to understand from a didactical point of view. (4) The problems connected with the inaccuracy of the mean motion that are typical for classical satellite theory are no longer present. The new elements are applied to analytical solutions of the zonal oblateness problem and to the problem of the 24 hour satellite.
Scheifele, G.↗
Canonical analysis for increased classification speed and channel selection
The quadratic form can be expressed as a monotonically increasing sum of squares when the inverse covariance matrix is represented in canonical form. This formulation has the advantage that, in testing a particular class hypothesis, computations can be discontinued when the partial sum exceeds the smallest value obtained for other classes already tested. A method for channel selection is presented which arranges the original input measurements in that order which minimizes the expected number of computations. The classification algorithm was tested on data from LARS Flight Line C1 and found to reduce the sum-of-products operations by a factor of 6.7 in comparison with the conventional approach. In effect, the accuracy of a twelve-channel classification was achieved using only that CPU time required for a conventional four-channel classification.
Eppler, W.↗
Canonical orbital elements in terms of an arbitrary independent variable
Within the framework of the Hamiltonian mechanics in the extended phase space, a set of canonical elements of the Delaunay type is developed in terms of an arbitary independent angular variable. Application to the four classical anomalies - eccentric, true, elliptic, and mean - is presented. Particular attention is given to the generalized time equation and its conjugate energy equation.
Bond, V. R.↗
Queueing analysis of a canonical model of real-time multiprocessors
A logical classification of multiprocessor structures from the point of view of control applications is presented. A computation of the response time distribution for a canonical model of a real time multiprocessor is presented. The multiprocessor is approximated by a blocking model. Two separate models are derived: one created from the system's point of view, and the other from the point of view of an incoming task.
Krishna, C. M.↗
On the control canonical structure of a class of scalar input systems
A discrete finite dimensional system, nonharmonic Fourier series and controllability, reduction to canonical form, and spectral synthesis are considered. The extent to which the eigenvalue associated with a controllable pair of a certain type may be modified via continuous linear state feedback is demonstrated.
Teglas, R.↗
Canonical solutions for unsteady flow fields
The initial value problem of one-dimensional gas-dynamics involving discontinuous, nonuniform initial data is discussed. Canonical solutions which are valid in a small x, t region aroung a discontinuity, and which include the first order effects of nonuniformities in the data, are derived explicitly. The theory is derived by considering a group of elementary piston problems. Solutions with a shock or with a centered expansion wave are worked out individually in order to relate initial flow properties and their gradients to the speed and acceleration of the discontinuity waves. They are then combined to represent the solution of a general initial value problem by regarding the piston path as a contact line. In addition, problems with chemical reaction are discussed in terms of elementary piston problems which involve strong detonation waves, Chapman-Jouguet detonation waves, and deflagration waves.
Liu, G. C.↗
On the control canonical structure of a class of scalar input systems
A discrete finite dimensional system, nonharmonic Fourier series and controllability, reduction to canonical form, and spectral synthesis are considered. The extent to which the eigenvalue associated with a controllable pair of a certain type may be modified via continuous linear state feedback is demonstrated. Previously announced in STAR as N83-28925
Teglas, R. G.↗
A comparison of the usefulness of canonical analysis, principal components analysis, and band selection for extraction of features from TMS data for landcover analysis
Three feature extraction methods, canonical analysis (CA), principal component analysis (PCA), and band selection, have been applied to Thematic Mapper Simulator (TMS) data in order to evaluate the relative performance of the methods. The results obtained show that CA is capable of providing a transformation of TMS data which leads to better classification results than provided by all seven bands, by PCA, or by band selection. A second conclusion drawn from the study is that TMS bands 2, 3, 4, and 7 (thermal) are most important for landcover classification.
Boyd, R. K.↗
A simple algorithm for computing canonical forms
It is well known that all linear time-invariant controllable systems can be transformed to Brunovsky canonical form by a transformation consisting only of coordinate changes and linear feedback. However, the actual procedures for doing this have tended to be overly complex. The technique introduced here is envisioned as an on-line procedure and is inspired by George Meyer's tangent model for nonlinear systems. The process utilizes Meyer's block triangular form as an intermedicate step in going to Brunovsky form. The method also involves orthogonal matrices, thus eliminating the need for the computation of matrix inverses. In addition, the Kronecker indices can be computed as a by-product of this transformation so it is necessary to know them in advance.
Ford, H.↗
A canonical expansion for nonlinear systems
The importance of differential geometry, particularly Lie brackets of vector fields, in the study of nonlinear systems is well established. Under very mild assumptions, it is shown that a real-analytic nonlinear system has an expansion in which the coefficients are computed in terms of Lie brackets. This expansion occurs in a special coordinate system. The concept of a pure feedback system is also explained. For control design involving a nonlinear system, one approach is to put the system in its canonical expansion and approximate by that part having only feedback paths.
Su, R.↗
Fifty Year Canon of Lunar Eclipses: 1986-2035
A complete catalog is presented, listing the general circumstances of every lunar eclipse from 1901 through 2100. To compliment this catalog, a set of figures illustrate the basic Moon-shadow geometry and global visibility for every lunar eclipse over the 200 year interval. Focusing in on the next fifty years, 114 detailed diagrams show the Moon's path through Earth's shadow during every eclipse, including contact times at each phase. The accompanying cylindrical projection maps of Earth show regions of hemispheric visibility for all phases. The appendices discuss eclipse geometry, eclipse frequency and recurrence, enlargement of Earth's shadow, crater timings, eclipse brightness and time determination. Finally, a simple FORTRAN program is provided which can be used to predict the occurrence and general characteristics of lunar eclipses. This work is a companion volume to NASA Reference Publication 1178: Fifty Year Canon of Solar Eclipses: 1986-2035.
Espenak, Fred↗
Alpha-canonical form representation of the open loop dynamics of the Space Shuttle main engine
A parameter and structure estimation technique for multivariable systems is used to obtain a state space representation of open loop dynamics of the space shuttle main engine in alpha-canonical form. The parameterization being used is both minimal and unique. The simplified linear model may be used for fault detection studies and control system design and development.
Duyar, Almet↗
Uncertainty relations, zero point energy and the linear canonical group
The close relationship between the zero point energy, the uncertainty relations, coherent states, squeezed states, and correlated states for one mode is investigated. This group-theoretic perspective enables the parametrization and identification of their multimode generalization. In particular the generalized Schroedinger-Robertson uncertainty relations are analyzed. An elementary method of determining the canonical structure of the generalized correlated states is presented.
Sudarshan, E. C. G.↗