scholarly journals Analytical solutions of a particular Hill's differential system

2019 ◽  
Vol 11 (1) ◽  
pp. 121-129
Author(s):  
Nicolae MARCOV
Keyword(s):  
Periodic Function ◽  
Numerical Solution ◽  
Explicit Form ◽  
Analytical Solutions ◽  
Fundamental Matrix ◽  
Continuous Periodic Function ◽  
Periodic Term ◽  
First Order ◽  
Analytical Functions ◽  
Periodic Equation

Consider a second order differential linear periodic equation. This equation is recast as a first-order homogeneous Hill’s system. For this system we obtain analytical solutions in explicit form. The first solution is a periodic function. The second solution is a sum of two functions; the first is a continuous periodic function, but the second is an oscillating function with monotone linear increasing amplitude. We give a formula to directly compute the slope of this increase, without knowing the second numerical solution. The periodic term of second solution may be computed directly. The coefficients of fundamental matrix of the system are analytical functions.

scholarly journals Numerical Solution of the Spinor-Spinor Bethe-Salpeter Equation in Functional Nonlinear Spinor Theory

1975 ◽  
Vol 30 (5) ◽  
pp. 656-671
Author(s):  
W. Bauhoff
Keyword(s):  
Angular Momentum ◽  
Excited State ◽  
Variational Method ◽  
Numerical Solution ◽  
High Precision ◽  
Nonlinear Spinor ◽  
Spinor Theory ◽  
First Order ◽  
Scalar Mesons ◽  
Functional Methods

AbstractThe mass eigenvalue equation for mesons in nonlinear spinor theory is derived by functional methods. In second order it leads to a spinorial Bethe-Salpeter equation. This is solved by a variational method with high precision for arbitrary angular momentum. The results for scalar mesons show a shift of the first order results, obtained earlier. The agreement with experiment is improved thereby. An excited state corresponding to the η' is found. A calculation of a Regge trajectory is included,too.

Mechanical analysis of shrink-fitted thick FG cylinders based on first order shear deformation theory and FE simulation

2021 ◽  
pp. 095440622110127
Author(s):  
Mohammad Reza Salehi Kolahi ◽  
Hossein Rahmani ◽  
Hossein Moeinkhah
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Fe Simulation ◽  
Shear Deformation Theory ◽  
Mechanical Analysis ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
First Order ◽  
Analytical Functions ◽  
Plane Elasticity Theory

In this paper, the first order shear deformation theory is used to derive an analytical formulation for shrink-fitted thick-walled functionally graded cylinders. It is assumed that the cylinders have constant Poisson’s ratio and the elastic modulus varies radially along the thickness with a power function. Furthermore, a finite element simulation is carried out using COMSOL Multiphysics, which has the advantage of defining material properties as analytical functions. The results from first order shear deformation theory are compared with the findings of both plane elasticity theory and FE simulation. The results of this study could be used to design and manufacture for elastic shrink-fitted FG cylinders.

scholarly journals ON CONDITIONING FOR A GENERAL SYSTEM OF FOUR POINT BOUNDARY VALUE PROBLEMS

1996 ◽  
Vol 27 (3) ◽  
pp. 219-225
Author(s):  
M. S. N. MURTY
Keyword(s):  
Differential Equation ◽  
Fundamental Matrix ◽  
Close Relationships ◽  
General System ◽  
Point Boundary ◽  
Matrix Differential Equation ◽  
Growth Behaviour ◽  
First Order ◽  
Matrix Differential ◽  
The Stability

In this paper we investigate the close relationships between the stability constants and the growth behaviour of the fundamental matrix to the general FPBVP'S associated with the general first order matrix differential equation.

scholarly journals Modified Decomposition Method with New Inverse Differential Operators for Solving Singular Nonlinear IVPs in First- and Second-Order PDEs Arising in Fluid Mechanics

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Nemat Dalir
Keyword(s):  
Fluid Mechanics ◽  
Analytical Solutions ◽  
Initial Value Problems ◽  
Decomposition Method ◽  
Differential Operators ◽  
Second Order ◽  
Nonlinear Pdes ◽  
Initial Value ◽  
Exact Analytical Solutions ◽  
First Order

Singular nonlinear initial-value problems (IVPs) in first-order and second-order partial differential equations (PDEs) arising in fluid mechanics are semianalytically solved. To achieve this, the modified decomposition method (MDM) is used in conjunction with some new inverse differential operators. In other words, new inverse differential operators are developed for the MDM and used with the MDM to solve first- and second-order singular nonlinear PDEs. The results of the solutions by the MDM together with new inverse operators are compared with the existing exact analytical solutions. The comparisons show excellent agreement.

scholarly journals Safety parameters calibration in the structural design of sewer liners

2018 ◽  
Vol 45 ◽  
pp. 00096
Author(s):  
Arkadiusz Szot
Keyword(s):  
Analytical Solutions ◽  
Structural Design ◽  
Safety Index ◽  
Safety Factors ◽  
Load Bearing Capacity ◽  
First Order Reliability Method ◽  
First Order ◽  
Reliability Method ◽  
Safety Parameters ◽  
Global Safety Factor

The article concerns aspects of safety in the process of designing continuous polymer liners used to strengthen and seal sewers and drains. The issues of safety coefficients, the variability of basic loadbearing parameters of liners and the problem of sensitivity of analytical solutions describing load-bearing capacity are discussed. The currently used magnitude of safety factors has been verified. The results of an examination on the safety index of liners for strengthening sewers has been presented in the paper. The necessity for the verification of current concepts of liner safety normalisation was herein addressed. A postulation to abandon the analogy of liners for newly constructed pipes was formulated. Calculations using the Hasofer-Lind safety index (First Order Reliability Method) were performed in some cases. A verification and evaluation of the global safety factor for sewer liners were herein carried out.

scholarly journals Modelling Very-High-Eccentricity Asteroidal Librations with the Andoyer Hamiltonian

1999 ◽  
Vol 172 ◽  
pp. 389-390
Author(s):  
A. Simula ◽  
S. Ferraz-Mello ◽  
C. Giordano
Keyword(s):  
Explicit Form ◽  
Main Part ◽  
Order Approximation ◽  
High Eccentricity ◽  
Order Resonance ◽  
First Order ◽  
Main Effect ◽  
Realistic Description ◽  
First Order Approximation ◽  
Very High

High-eccentricity asteroidal librations are modelled using the high-eccentricity non-planar asymmetric expansion (Roig et al 1997). This second-degree expansion gives us the potential of the perturbing forces acting on a resonant asteroid in a first order resonance in explicit form, as a quadratic polynomial in the canonical non-singular variables. Secular and short periodic perturbations are introduced in the model, giving a more realistic description of the dynamics.The reducing Sessin’s transformation (Sessin, 1981; Sessin & Ferraz-Mello, 1984) is used to include the main effect of Jupiter’s ecc entricity in the main part of the Hamiltonian. It leads to an integrable first-order approximation known as the second fundamental model for resonance (Henrard & Lemaitre 1983) or Andoyer Hamiltonian (Andoyer 1903).

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