Asymptotic approaches in mechanics: New parameters and procedures-Reference-Cited by-同舟云学术

Asymptotic approaches in mechanics: New parameters and procedures

Published:2003-01-01 Issue:1 Volume:56 Page:87-110
ISSN:0003-6900
Container-title:Applied Mechanics Reviews
language:en
Short-container-title:

Author:

Andrianov Igor V¹,Awrejcewicz Jan²,Barantsev Rem G³

Affiliation:

1. Institut fu¨r Allegmeine Mechanik, RWTH Aachen, Templergraben 64, D-52056 Aachen, Germany; igor_andrianov@hotmail.com

2. Technical University of Ło´dz´, Department of Automatics and Biomechanics, 1/15 Stefanowskiego St., 90-924 Ło´dz´, Poland; awrejcew@ck-sg.p.lodz.pl

3. St. Petersburg State University, Box 159, 195256, St. Petersburg, Russia; brem@mail.ru

Abstract

This survey is devoted to recent achievements in the field of asymptotic approaches. Here we consider the asymptotics in relation to completely new and sometimes unexpected parameters. Some procedures leading to improvement and isolation of the essential analytical structure of the perturbation series are presented. It is also shown that many problems of perturbation theory, which seem to be relatively simple at a first glance, are still far from completely solved. Different asymptotic techniques to solve the same problem and their influence on the results are briefly illustrated and discussed. This review paper contains 310 references.

Publisher

ASME International

Subject

Mechanical Engineering

Link

http://asmedigitalcollection.asme.org/appliedmechanicsreviews/article-pdf/56/1/87/5439617/87_1.pdf

Reference312 articles.

1. Andrianov IV and Awrejcewicz J (2001a), New trends in asymptotic approaches: summation and interpolation methods, Appl. Mech. Rev. 54(1), 69–92.

2. Andrianov IV and Awrejcewicz J (2001b), Asymptotic approaches to simplified boundary value problems of non-linear dynamics, Nonlinear Analysis, 47, 2261–2269.

3. Andrianov IV and Manevitch LI (1992), Asymptotology: Problems, ideas and results, J Natural Geometry 2(2), 137–150.

4. Andrianov IV and Manevitch LI (1994), Asymptotology: Ideas, Methods, Results (in Russian), Aslan, Moscow.

5. Barantsev RG (1989), Asymptotic versus Classical Mathematics, Topics in Mathematical Analysis, World Scientific, Singapore, 49–64.

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