A Small-Parameter Method for I. Vekua’s Nonlinear and Nonshallow Shells

2008 ◽  
pp. 155-166
Author(s):  
Tengiz Meunargia
Keyword(s):  
Small Parameter ◽  
Parameter Method ◽  
Small Parameter Method

scholarly journals On the Solution of the Exterior Boundary Value Problem with the Aid of Series

1978 ◽  
Vol 41 ◽  
pp. 175-176
Author(s):  
M. S. Petrovskaya
Keyword(s):  
Gravitational Field ◽  
Boundary Value Problem ◽  
Small Parameter ◽  
Integral Equations ◽  
Boundary Value ◽  
Parameter Method ◽  
Small Parameter Method ◽  
Exterior Boundary ◽  
Exterior Boundary Value Problem ◽  
Molodensky Problem

AbstractThe exterior gravitational field depending on the Earth’s non-sphericity is usually determined from the analysis of satellite data or by the solution of the exterior boundary value problem. In the latter case some integral equations are solved which correlate the exterior potential with the known vector of gravity and the shape of the Earth’s surface (molodensky problem). In order to carry out the integration the small parameter method is applied. As a result, all the quantities which involve the equations should be expanded in powers of a certain small parameter, among these being the heights of the Earth’s surface points as well as the inclination α of the Earth’s physical surface. Since the angle α can be significant, especially in mountains, and in fact does not depend on any small parameter then the solution of integral equations is possible only for the Earth’s surface which is smoothed enough.

scholarly journals Solving a Problem of Rotary Motion for a Heavy Solid Using the Large Parameter Method

2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
A. I. Ismail
Keyword(s):  
Angular Velocity ◽  
Small Parameter ◽  
Initial Conditions ◽  
Geometric Interpretation ◽  
Rigid Bodies ◽  
Parameter Method ◽  
Large Parameter ◽  
Small Parameter Method ◽  
Rotational Motions ◽  
The Stability

The small parameter method was applied for solving many rotational motions of heavy solids, rigid bodies, and gyroscopes for different problems which classify them according to certain initial conditions on moments of inertia and initial angular velocity components. For achieving the small parameter method, the authors have assumed that the initial angular velocity is sufficiently large. In this work, it is assumed that the initial angular velocity is sufficiently small to achieve the large parameter instead of the small one. In this manner, a lot of energy used for making the motion initially is saved. The obtained analytical periodic solutions are represented graphically using a computer program to show the geometric periodicity of the obtained solutions in some interval of time. In the end, the geometric interpretation of the stability of a motion is given.

Numerical small parameter method for stiff ODE:s

1983 ◽  
Vol 23 (1) ◽  
pp. 118-131 ◽  
Author(s):  
Tian-Min Han
Keyword(s):  
Small Parameter ◽  
Parameter Method ◽  
Small Parameter Method

scholarly journals Investigation of bending of an elastically supported beam taking into account the inhomogeneity of the base

2020 ◽  
pp. 190-193
Author(s):  
Надежда Витальевна Минаева ◽  
Денис Викторович Сабынин ◽  
Александр Иванович Шашкин
Keyword(s):  
Small Parameter ◽  
Fourth Order ◽  
Elastic Base ◽  
Parameter Method ◽  
Small Parameter Method ◽  
Convergence Region ◽  
Small Parameters ◽  
Set Up ◽  
Elastically Supported ◽  
Fixed Beam

Рассмотрен изгиб шарнирно закрепленной балки на упругом основании. Начальный прогиб и неоднородность жесткости основания заданы с точность до малых параметров. Получено условие, определяющее границу области сходимости метода малого параметра. Найдена функция, характеризующая прогиб, с точностью до величин четвертого порядка малости. Проанализирован случай, когда малые параметры являются случайными величинами. The bending of a pivotally fixed beam on an elastic base is considered. The initial deflection and inhomogeneity of the base stiffness are set up to small parameters. A condition is obtained that defines the boundary of the convergence region of the small parameter method. A function describing the deflection is found up to the fourth order of smallness. The case when small parameters are random variables is analyzed.

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