Determination of lie-bäcklund symmetries of differential equations using formac

1986 ◽  
Vol 39 (1) ◽  
pp. 93-103 ◽  
Author(s):  
R.N. Fedorova ◽  
V.V. Kornyak
Keyword(s):  
Differential Equations ◽  
Symmetries Of Differential Equations

MODELING OF NONLINEAR VIBRATION PROBLEMS WITH FLUID FLOWS THROUGH PIPELINES

2018 ◽  
pp. 44-47
Author(s):  
F.J. Тurayev
Keyword(s):  
Differential Equations ◽  
Nonlinear Vibration ◽  
Viscoelastic Properties ◽  
Construction Material ◽  
Fluid Flows ◽  
Variable Coefficients ◽  
Algebraic Equations ◽  
Flowing Liquid ◽  
Vibration Problems

In this paper, mathematical model of nonlinear vibration problems with fluid flows through pipelines have been developed. Using the Bubnov–Galerkin method for the boundary conditions, the resulting nonlinear integro-differential equations with partial derivatives are reduced to solving systems of nonlinear ordinary integro-differential equations with both constant and variable coefficients as functions of time.A system of algebraic equations is obtained according to numerical method for the unknowns. The influence of the singularity of heredity kernels on the vibrations of structures possessing viscoelastic properties is numerically investigated.It was found that the determination of the effect of viscoelastic properties of the construction material on vibrations of the pipeline with a flowing liquid requires applying weakly singular hereditary kernels with an Abel type singularity.

scholarly journals Projective Collineations of Decomposable Spacetimes Generated by the Lie Point Symmetries of Geodesic Equations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1018
Author(s):  
Andronikos Paliathanasis
Keyword(s):  
Differential Equations ◽  
Riemannian Space ◽  
Dimensional Subspace ◽  
Geometric Construction ◽  
Lie Point Symmetries ◽  
Geodesic Equations ◽  
Symmetries Of Differential Equations ◽  
Projective Collineations

We investigate the relation of the Lie point symmetries for the geodesic equations with the collineations of decomposable spacetimes. We review previous results in the literature on the Lie point symmetries of the geodesic equations and we follow a previous proposed geometric construction approach for the symmetries of differential equations. In this study, we prove that the projective collineations of a n+1-dimensional decomposable Riemannian space are the Lie point symmetries for geodesic equations of the n-dimensional subspace. We demonstrate the application of our results with the presentation of applications.

scholarly journals Contact Symmetries of a Model in Optimal Investment Theory

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 217
Author(s):  
Daniel J. Arrigo ◽  
Joseph A. Van de Grift
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Governing Equation ◽  
Optimal Investment ◽  
Original Equation ◽  
Case Scenario ◽  
Investment Theory ◽  
Symmetries Of Differential Equations ◽  
Contact Symmetry ◽  
Terminal Value Problem

It is generally known that Lie symmetries of differential equations can lead to a reduction of the governing equation(s), lead to exact solutions of these equations and, in the best case scenario, lead to a linearization of the original equation. In this paper, we consider a model from optimal investment theory where we show the governing equation possesses an extensive contact symmetry and, through this, we show it is linearizable. Several exact solutions are provided including a solution to a particular terminal value problem.

Determination of Stresses in Cemented Lap Joints

1953 ◽  
Vol 20 (3) ◽  
pp. 355-364
Author(s):  
R. W. Cornell
Keyword(s):  
Differential Equations ◽  
Infinite Number ◽  
Lap Joints ◽  
The Other ◽  
Complete Analysis ◽  
Stress Distributions ◽  
Lap Joint ◽  
Analogy Method ◽  
Set Up

Abstract A variation and extension of Goland and Reissner’s (1) method of approach is presented for determining the stresses in cemented lap joints by assuming that the two lap-joint plates act like simple beams and the more elastic cement layer is an infinite number of shear and tension springs. Differential equations are set up which describe the transfer of the load in one beam through the springs to the other beam. From the solution of these differential equations a fairly complete analysis of the stresses in the lap joint is obtained. The spring-beam analogy method is applied to a particular type of lap joint, and an analysis of the stresses at the discontinuity, stress distributions, and the effects of variables on these stresses are presented. In order to check the analytical results, they are compared to photoelastic and brittle lacquer experimental results. The spring-beam analogy solution was found to give a fairly accurate presentation of the stresses in the lap joint investigated and should be useful in analyzing other cemented lap-joint structures.

Determination of Nonchaotic Behavior for Some Classes of Polynomial Jerk Equations

2020 ◽  
Vol 30 (08) ◽  
pp. 2050117
Author(s):  
Marcelo Messias ◽  
Rafael Paulino Silva
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Simple Form ◽  
Chaotic Dynamics ◽  
Third Order ◽  
Algebraic Criterion

In this work, by using an algebraic criterion presented by us in an earlier paper, we determine the conditions on the parameters in order to guarantee the nonchaotic behavior for some classes of nonlinear third-order ordinary differential equations of the form [Formula: see text] called jerk equations, where [Formula: see text] is a polynomial of degree [Formula: see text]. This kind of equation is often used in literature to study chaotic dynamics, due to its simple form and because it appears as mathematical model in several applied problems. Hence, it is an important matter to determine when it is chaotic and also nonchaotic. The results stated here, which are proved using the mentioned algebraic criterion, corroborate and extend some results already presented in literature, providing simpler proofs for the nonchaotic behavior of certain jerk equations. The algebraic criterion proved by us is quite general and can be used to study nonchaotic behavior of other types of ordinary differential equations.

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