Flows near isolated invariant sets in dimension 3
Flows on 3-manifolds near isolated invariant sets
Easton, R.↗
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Isolated invariant sets and isolating blocks
Closed invariant sets of smooth flow on compact manifold involving homoclinic or heteroclinic point theory of Poincare
Conley, C.↗
An invariance principle for dynamical systems on Banach space - Application to the general problem of thermoelastic stability
Thermoelastic stability as function of thermodynamic properties of elastic materials, applying invariance principle to dynamical systems on Banach space
Infante, E. F.↗
Theoretical frameworks for testing relativistic gravity. III - Conservation laws, Lorentz invariance, and values of the PPN parameters
Lorentz invariant theory for relativistic gravity testing, deriving conservation laws and parameter constraints from parametrized post-Newtonian equations of motion
Will, C. M.↗
Adiabatic invariance
Theoretical work designed to bridge the gap between celestial mechanics and the motion of charged particles in magnetic fields is presented. Attempts are made to devise a simple uninvolved method to solve adiabatic invariant motion problems. The method is illustrated by solving a problem involving the motion of a slowly perturbed harmonic oscillator.
Stern, D.↗
An invariant second-order closure model of the compressible turbulent boundary layer on a flat plate
The development of an invariant model designed expressly for the computation of shear flows is discussed. The model for incompressible layers seeks a second-order closure of the equations for the mean and fluctuating fields. The development of a method for computing the behavior of shear layers in compressible forces is described. The complexity of the analysis is restrained by limiting the consideration to a flat plate boundary layer where the mean pressure can be taken to be constant.
Donaldson, C. D.↗
On the input-output properties of linear time-invariant systems.
Recently improved sufficient conditions for the Lp stability of multiple-input multiple-output linear time-invariant feedback systems are given. The continuous-time case is done in detail; the discrete-time case is outlined. Unstable open-loop systems with singular residue matrices are allowed.
Desoer, C. A.↗
A pictorial study of an invariant torus in phase space of four dimensions.
An investigation was conducted with the aid of a computer graphics device at Goddard Space Flight Center to study the behavior of the invariant manifolds of a particular fourth-order equation, as a parameter in the equation is varied over the interval from 0 to 1. The equation consists of two coupled Van der Pol equations. For a small parameter value, the manifold is an asymptotically stable torus, where the flow on the torus is simply a rotation. As the value of the parameter is increased, the only thing that changes is the nature of the flow on the torus, which itself persists throughout the parameter variation. It is shown that ultimately the four periodic cycles which appear play a more significant part in the phase profile of the system than does the torus itself.
Baxter, R.↗
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.↗
A linear shift-invariant image preprocessing technique for multispectral scanner systems
A linear shift-invariant image preprocessing technique is examined which requires no specific knowledge of any parameter of the original image and which is sufficiently general to allow the effective radius of the composite imaging system to be arbitrarily shaped and reduced, subject primarily to the noise power constraint. In addition, the size of the point-spread function of the preprocessing filter can be arbitrarily controlled, thus minimizing truncation errors.
Mcgillem, C. D.↗
Modeling of linear time-varying systems by linear time-invariant systems of lower order.
A method for modeling linear time-varying differential systems by linear time-invariant systems of lower order is proposed, extending the results obtained by Bierman (1972) by resolving such qualities as the model stability, various possible models of differing dimensions, and the uniqueness or nonuniqueness of the model coefficient matrix. In addition to the advantages cited by Heffes and Sarachik (1969) and Bierman, often by modeling a subsystem of a larger system it is possible to analyze the overall system behavior more easily, with resulting savings in computation time.
Nosrati, H.↗
Orientational invariance of the rotational transition probability in the sudden approximation
Semiclassical collisions of an atom with a rigid-rotor molecule are examined in the sudden approximation. The rotational transition probability is shown to be invariant with respect to the choice of orientation for the molecular coordinate system; this fact contradicts recently reported results of a computer analysis. The present analysis may lead to an improved interpretation of recent molecular beam measurements.
Stallcop, J. R.↗
Conformal invariance and Hamilton Jacobi theory for dissipative systems
For certain dissipative systems, a comparison can be made between the Hamilton-Jacobi theory and the conformal invariance of action theory. The two concepts are not identical, but the conformal action theory covers the Hamilton-Jacobi theory.
Kiehn, R. M.↗
Storm-associated variations of equatorially mirroring ring current protons, 1-800 keV, at constant first adiabatic invariant
Explorer 45 observations of ring current protons mirroring near the equator, 1-800 keV, are presented at constant first adiabatic invariant mu throughout the period of the December 17, 1971, geomagnetic storm. The parameter mu is obtained from simultaneous magnetic field and particle observations. Particle deceleration in response to the storm time magnetic field decrease causes ring current measurements viewed at constant energy to underestimate the storm time increase in proton intensities at energies not exceeding 200 keV. This adiabatic deceleration also accounts for the large flux decreases observed at energies above 200 keV during the storm, in contradiction with previous results (Soraas and Davis, 1968) obtained using a model for the storm time magnetic field.
Lyons, L. R.↗
Essential uncontrollability of discrete linear, time-invariant, dynamical systems
The concept of a 'best approximating m-dimensional subspace' for a given set of vectors in n-dimensional whole space is introduced. Such a subspace is easily described in terms of the eigenvectors of an associated Gram matrix. This technique is used to approximate an achievable set for a discrete linear time-invariant dynamical system. This approximation characterizes the part of the state space that may be reached using modest levels of control. If the achievable set can be closely approximated by a proper subspace of the whole space then the system is 'essentially uncontrollable'. The notion finds application in studies of failure-tolerant systems, and in decoupling.
Cliff, E. M.↗
Invariants of optimal minimal-order observer-based compensators
The relations characterizing the optimal minimal-order observer-based compensators for a linear time-invariant multivariable system in a certain canonical form, with a random initial state (or equivalently, known initial state with white driving noise) have been reported by Miller and independently by others. In this note, we establish in general that the plant transfer function uniquely determines the optimal compensator transfer function, and that this characterizes precisely the degrees of freedom in the compensator design. Any two realizations of the optimal compensator dynamics yield the same performance.
Blanvillain, P.↗
Thermal microwave emission from a random inhomogeneous layer over a homogeneous medium using the method of invariant imbedding
The paper studies thermal microwave emission from an inhomogeneous slab of a random medium, with possible nonuniform absorption, scattering, and temperature profiles, bounded by different dielectrics on both sides. The invariant imbedding method is used to cast the boundary value problem of the radiative transfer equations into an initial value problem at zero slab thickness. As a numerical example, the angular and polarization variations of brightness temperatures for ice over water are considered.
Tsang, L.↗
Invariants of optimal minimal-order observer-based compensators
The relations characterizing the optimal minimal-order observer-based compensators for a linear time-invariant multivariable system with a random initial state (or, equivalently, known initial state and white plant-driving noise) have been reported by Miller (1973). In this note we establish in general that the plant transfer function uniquely determines the optimal compensator transfer function, and that this characterizes precisely the degrees of freedom in the compensator design; computational implications of this result are indicated.
Blanvillain, P. J.↗