Nonlinear Mechanics, Groups and Symmetry (Mathematics and Its Applications, 319)

Mitropolsky, Yuri A.; Lopatin, A.K.

ISBN 10: 079233339X / ISBN 13: 9780792333395

Published by Springer, 1995

About this Item

Seller Inventory # ABLIING23Feb2416190181762

Bibliographic Details

• Title: Nonlinear Mechanics, Groups and Symmetry (Mathematics and Its Applications, 319)
• Publisher: Springer
• Publication Date: 1995
• Language: English
• ISBN 10: 079233339X
• ISBN 13: 9780792333395
• Binding: Hardcover
• Condition: New

About this title

Synopsis

Asymptotic methods of nonlinear mechanics developed by N. M. Krylov and N. N. Bogoliubov originated new trend in perturbation theory. They pene­ trated deep into various applied branches (theoretical physics, mechanics, ap­ plied astronomy, dynamics of space flights, and others) and laid the founda­ tion for lrumerous generalizations and for the creation of various modifications of thesem. E!f,hods. A great number of approaches and techniques exist and many differen. t classes of mathematical objects have been considered (ordinary differential equations, partial differential equations, delay diffe,'ential equations and others). The stat. e of studying related problems was described in mono­ graphs and original papers of Krylov N. M. , Bogoliubov N. N. [1], [2], Bogoli­ ubov N. N [1J, Bogoliubov N. N. , Mitropolsky Yu. A. [1], Bogoliubov N. N. , Mitropol­ sky Yu. A. , Samoilenko A. M. [1], Akulenko L. D. [1], van den Broek B. [1], van den Broek B. , Verhulst F. [1], Chernousko F. L. , Akulenko L. D. and Sokolov B. N. [1], Eckhause W. [l], Filatov A. N. [2], Filatov A. N. , Shershkov V. V. [1], Gi­ acaglia G. E. O. [1], Grassman J. [1], Grebennikov E. A. [1], Grebennikov E. A. , Mitropolsky Yu. A. [1], Grebennikov E. A. , Ryabov Yu. A. [1], Hale J . K. [I]' Ha­ paev N. N. [1], Landa P. S. [1), Lomov S. A. [1], Lopatin A. K. [22]-[24], Lykova O. B.

Synopsis

This unique monograph deals with the development of asymptotic methods of perturbation theory, making wide use of group-theoretical techniques. Various assumptions about specific group properties are investigated, and are shown to lead to modifications of existing methods, such as the Bogoliubov averaging method and the Poincare - Birkhoff normal form, as well as to the formulation of new ones. The development of normalization techniques of Lie groups is also treated. The wealth of examples demonstrates how these new group theoretical techniques can be applied to analyze specific problems. This book will be of interest to researchers and graduate students in the field of pure and applied mathematics, mechanics, physics, engineering, and biosciences.