On a symbolic algebra for Hencky-Prandtl nets

1983 ◽  
Vol 94 (2) ◽  
pp. 341-350
Author(s):  
R. Hill
Keyword(s):  
General Solution ◽  
Boundary Value Problems ◽  
Classical Theory ◽  
Systematic Approach ◽  
Standard Technique ◽  
Field Equations ◽  
Infinite Matrices ◽  
Symbolic Algebra ◽  
Series Representations ◽  
Plane Deformations

AbstractIn the classical theory of plane deformations in isotropic plastic media, the field equations are hyperbolic and the orthogonal families of characteristics are known as Hencky-Prandtl nets. Their distinctive geometry has been given symbolic expression by Collins (1968), in an algebra of infinite matrices associated with canonical series representations of the general solution. This has become the standard technique when investigating boundary-value problems, both analytically and numerically. The basic framework of the algebra is here reorganized and developed. A systematic approach then leads to new identities which are shown to be fundamental in the algebraic hierarchy.

scholarly journals Wormholes in Wyman's solution

2014 ◽  
Vol 23 (11) ◽  
pp. 1450086 ◽  
Author(s):  
J. B. Formiga ◽  
T. S. Almeida
Keyword(s):  
Scalar Field ◽  
General Solution ◽  
Detailed Analysis ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Human Beings ◽  
Einstein Field Equations ◽  
Field Equations

The most general solution of the Einstein field equations coupled with a massless scalar field is known as Wyman's solution. This solution is also present in the Brans–Dicke theory and, due to its importance, it has been studied in detail by many authors. However, this solutions has not been studied from the perspective of a possible wormhole. In this paper, we perform a detailed analysis of this issue. It turns out that there is a wormhole. Although we prove that the so-called throat cannot be traversed by human beings, it can be traversed by particles and bodies that can last long enough.

Slow stationary sources

2021 ◽  
pp. 56-64
Author(s):  
Andrew M. Steane
Keyword(s):  
General Solution ◽  
Speed Of Light ◽  
Field Equations ◽  
Vector Potentials ◽  
Linearized Theory ◽  
Stationary Sources ◽  
Metric Perturbation

The linearized theory is applied to sources such as ordinary stars whose speed is small compared to the speed of light. This yields the “gravitoelectromagnetic” theory. The gravitoelectromagnetic field equations are obtained, along with their general solution via scalar and vector potentials. It is shown how to calculate the metric perturbation, and hence the field, due to a rotating ring or a ball, and thus how to calculate orbits, timing, and the Lense-Thirring precession.

On Realization of Program Constraints: Part I—Theory

1989 ◽  
Vol 56 (3) ◽  
pp. 676-679 ◽  
Author(s):  
Jan Parczewski ◽  
Wojciech Blajer
Keyword(s):  
General Solution ◽  
Classical Theory ◽  
Theory Approach ◽  
Adequate Control ◽  
Control Forces ◽  
Program Constraint

The problem of realization of program constraints is considered. The classical theory approach based on replacing the constriant reactions by adequate control forces has been generalized to the case when the control forces are not collinear with program constraint vectors or, in the extreme, when the control forces do not project in these directions at all (control forces are tangent to constraint manifolds). A classification of possible ways of program constraint realization is proposed and a general solution of the problem is presented.

scholarly journals A note on de Sitter type solutions of Einstein's field equations

1967 ◽  
Vol 7 (4) ◽  
pp. 429-432
Author(s):  
A. H. Klotz
Keyword(s):  
General Solution ◽  
De Sitter ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Einstein's Field Equations

A method of deriving a class of solutions of Einstein's field equations with symmetry of de Sitter type is investigated, and the most general solution of this kind is derived.

The general axially symmetric static solution of Einstein’s vacuum field equations

1982 ◽  
Vol 382 (1783) ◽  
pp. 467-470 ◽  
Keyword(s):  
General Solution ◽  
Potential Function ◽  
Line Element ◽  
Static Solution ◽  
Vacuum Field ◽  
Axially Symmetric ◽  
Field Equations ◽  
Axis Of Symmetry ◽  
Axisymmetric Solutions ◽  
Associated Function

The general solution in closed form, including all the static axisymmetric solutions of Weyl, is presented in the canonical coordinates ρ and z of his line element. This general solution is constructed from an arbitrary function f ( z ), which coincides with his potential function along the axis of symmetry. To illustrate how the solution may be used, a particular function f , one resulting from a Newtonian solution, is used to find both the potential function and its associated function in the line element.

scholarly journals On inversion in the case of the fundamentally finite integrable Vekua complex differential equation

2020 ◽  
Vol 108 (122) ◽  
pp. 13-22
Author(s):  
Milos Canak ◽  
Miloljub Albijanic
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
General Solution ◽  
Boundary Value Problems ◽  
Imaginary Part ◽  
Boundary Value ◽  
The Real ◽  
Complex Differential Equation ◽  
The Core ◽  
Vekua Equation

The class of so called fundamentally finite integrable Vekua CDE is defined using the fixed point of the inversion and where one solution is equal to the coefficient of the equation. Then the different manifestations of inversion in relation to the general solution, an arbitrary analytical function inside and the core of the coefficient are examined. It shows that all the major problems of the Vekua equation theories, including boundary value problems can be interpreted and solved using the principle of inversion. The main significance of the fundamentally finite integrable Vekua equation is that the real and imaginary part of the solution can be separated, which in many mechanical and technique problems have certain physical meanings.

scholarly journals T -model field equations: The general solution

2021 ◽  
Vol 104 (6) ◽  
Author(s):  
Joan Josep Ferrando ◽  
Salvador Mengual
Keyword(s):  
General Solution ◽  
Field Equations ◽  
Model Field
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