Giải toán trực tuyến W | A




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Giải toán trực tuyến W|A

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Thứ Năm, 16 tháng 7, 2009

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THE SOLUTION STABILITY OF VAN DER POL'S EQUATION .

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 United States License.


THE SOLUTION STABILITY OF VAN DER POL'S EQUATION .




THE SOLUTION STABILITY OF

VAN DER POL'S EQUATION .

by CO. H . TRAN .


HUI - NCU HCMC

Vietnam coth123@math.com & cohtran@math.com Copyright 2004 November 06 2004 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------ ** Abstract : The Van der Pol differential quation is solved by averaging method . ** Subjects: Vibration Mechanics , The Differential equations . ------------------------------------------------------------------------------------------------------------------------------------------------------------------------Introduction This worksheet demonstrates Maple's capabilities in finding the graphical solution and dealing with the stability of the steady state solution of Van der Pol 's differential equation . All rights reserved. Copying or transmitting of this material without the permission of the authors is not allowed . We consider the Van Der Pol differential equation :
[0] Two topics that we will be in discussion are - Finding the steady state solution of this equation by averaging method .- Estimating the stability of solution obtained . 1 .Define the model of problem : We examine the effect of non-linear system under external force caused by the AC generator ( see fig 1. )Image Image( fig 1. ) The differential equation of this model is given in the form + [1] After simplifying we obtain : [2]


Chủ Nhật, 23 tháng 9, 2007

THE SOLUTION OF A VARIABLE BOUNDARY PROBLEM

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 United States License.


THE SOLUTION OF A VARIABLE BOUNDARY PROBLEM
Copyright 2007



August 16 2007
NOTE:
This worksheet demonstrates Maple's capabilities in researching the numerical and graphical solution of the variable boundary problem of a thick-walled cylinder of material enclosed in a thin metallic shell .
All rights reserved. Copying or transmitting of this material without the permission of the authors is not allowed .
Abstract :
The relations between stress and strain in linear viscoelastic theory are discussed from the viewpoint of application to problems of stress analysis. This consideration includes some important differences from the estimation of linear viscoelastic laws for the representation of material properties , and the integral operators expressing the creep function or relaxation function can be applied . By using of the differential operator for the relation between stress and strain it is usually most convenient to solve some problems which have the variable boundary .


REFERENCES
[1] ю.н. РАБОТНОВ , Пoлзyчесть элементов конструкций , издательство “наука” , MOCKBA 1966
[2] Lee E .H ., Radok J.R.M., Woodward W.B., Stress Analysis for Linear Viscoelastic Materials , Trans. Soc. Rheol., 3, 41-59 (1959)
Disclaimer: While every effort has been made to validate the solutions in this worksheet, the author is not responsible for any errors contained and are not liable for any damages resulting from the use of this material.

Legal Notice: The copyright for this application is owned by the author(s). Neither Maplesoft nor the author are responsible for any errors contained within and are not liable for any damages resulting from the use of this material. This application is intended for non-commercial, non-profit use only. Contact the author for permission if you wish to use this application in for-profit activities.






Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 United States License.

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 Toán học thuần túy, theo cách của riêng nó, là thi ca của tư duy logic. 
 Pure mathematics is, in its way, the poetry of logical ideas. 
 Albert Einstein .


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