Methods of asymptotic analysis and synthesis in the nonlinear dynamics and mechanics of deformable solids (Q2841475)

The book describes in detail the modern asymptotic methods widely used in nonlinear and solid body mechanics. To a great extent, the presentation is based on the results obtained by the authors in numerous papers cited in the book. The general approaches are first illustrated by simple examples, so that the reader can easily follow the main ideas of the methods. Thus the book is especially well suited for people with a background in mechanics who do not wish to become involved in much formal mathematics. The material is divided as follows:NEWLINENEWLINE Introduction. From idealization principles to the ``asymptotology''. Ch.~1. Asymptotic approximations and series. Ch.~2. Regular asymptotic expansions. Ch.~3. Singular asymptotic expansions. Ch.~4. The method of dynamic boundary effect. Ch.~5. Continualization. Ch.~6. Averaging and homogenization methods. Ch.~7. Summation of asymptotic series. Ch.~8. The use of Padé approximation. Ch.~9. Matched asymptotic expansions. Conclusion: Merits and disadvantages of asymptotic methods. References (377 items), subject and author indices.NEWLINENEWLINE One of the main purposes of the authors is to demonstrate that the computer revolution and the rapid growth of computer-assisted numerical methods do not depreciate the asymptotic methods. On the contrary, a reasonable combination of numerical and asymptotic methods can lead to real progress in nonlinear dynamics.NEWLINENEWLINE The book is prepared as a valuable contribution to the state-of-the-art on asymptotic methods in modern mechanics, and it will be of interest to students and researchers in the fields of mechanics and applied mathematics.