Showing papers on "Degrees of freedom published in 1971"

Gravitational degrees of freedom and the initial-value problem

Abstract: It is shown that for every spacelike three-geometry there exists a symmetric tensor that is (1) defined locally using only the three-metric and its derivatives, (2) conformally invariant, (3) traceless, and (4) covariantly divergence free ("transverse"). As a result, the arbitrarily specifiable (unconstrained) initial-value data in the Einstein initial-value problem for gravity can be completely characterized by a pair of symmetric, transverse, traceless tensors.

On Representations of the Doubly Non-Central F Distribution

Abstract: The cumulative doubly non-central F-distribution associated with the random variable F″ = mS1/nS2 is considered where S1 and S2 are two independent non-central chi-square varites with degrees of freedom n and m and non-centrality parameters λ1 and λ2, respectively. Representations in terms of series are presented together with efficient computational procedures for the special functions used in numerical evaluation.

A refined curved element for thin shells of revolution

Abstract: A refined axisymmetric curved finite element for the analysis of thin elastic-plastic shells of revolution is described in the paper. The improved element is obtained by employing cubic polynomials in terms of local Cartesian co-ordinates for the assumed in-plane and out-of-plane displacements. This introduces into the solution two internal degrees of freedom in the cord direction of each element. These internal degrees of freedom are removed by static condensation before assembling the individual element stiffness matrices, and are subsequently recovered after the nodal displacements are obtained. On comparison with the previous formulation, this procedure greatly improves the accuracy of the solution especially with regards to in-plane stress-resultants at discontinuities in the meridional curvature and interelement equilibrium of forces. The latter fact makes it possible to analyse shells with a discontinuous meridional slope. In using this element, improvement in the convergence of the elastic-plastic solutions has also been observed. Several examples illustrate the quality of solutions. The reported study is limited to axisymmetric loadings cum boundary conditions.

Spin waves and the BCS model

Abstract: We discuss the behaviour of the BCS model in the limit of infinitely many degrees of freedom. A new limiting procedure, based on spin waves, is proposed, by which the usual convergence difficulties can be overcome.

Contributions to the Determination of the Equations of Motion for Multidegree of Freedom Systems

Abstract: This paper is a further development of the kinematic problem presented in our 1967 paper [1] in which we have obtained the transmission functions for different orders of plane systems with many degrees of freedom. This paper establishes the corresponding system of differential equations of motion beginning with these functions. The purpose of this paper is to facilitate computer programming. Our study is based on the work of R. Beyer [2, 3] and is the first original addition to his papers. A second original contribution to Beyer’s theories is the deductive method of solution, from general to particular, which we have, incorporated in our work. Beyer concluded that the cases having two or three degrees of freedom can be considered as particular solutions to the results obtained.

Feedback Stabilization of Distributive Systems with Applications to Plasma Stabilization

Abstract: Theories for the feedback stabilization and control of dynamical systems with finite degrees of freedom have been extensively developed. The extension of some of these theories to systems with infinite degrees of freedom has been made only recently [1–2]. In the area of plasma stabilization, most studies have been associated with various thermonuclear plasma confinement schemes involving static magnetic field configurations or specified forms of high-frequency electromagnetic fields [3–6]. Recently, attempts have been made in using feedback to suppress certain forms of plasma oscillations [7–11] and to stabilize the unstable equilibria of hydromagnetic systems [12]. An important advantage of this approach is that the undesirable effects of system parameter variations may be reduced with the proper introduction of feedback and thereby relaxing the required tolerances in the system components such as the confining magnetic field structures. Further studies in this approach may lead to alternate practical means of plasma stabilization.

Model for machine-pile foundation-soil system

Abstract: A new method is presented herein considering the machine-pile foundation-soil system to act with two degrees of freedom, and taking into account the masses of the pile and the soil.