Ebook: Variational Principles of Continuum Mechanics with Engineering Applications: Volume 1: Critical Points Theory
Author: Vadim Komkov (auth.)
- Tags: Analysis
- Series: Mathematics and Its Applications 24
- Year: 1986
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Content:
Front Matter....Pages i-viii
Introduction....Pages 1-2
Energy Methods, Classical Calculus of Variations Approach — Selected Topics and Applications....Pages 3-106
The Legendre Transformation, Duality and Functional Analytic Approach....Pages 107-205
Some Known Variational Principles In Elasticity....Pages 206-245
Variational Formulation of Problems of Elastic Stability. Topics in the Stability of Beams and Plates....Pages 246-312
An Example of a Variational Approach to Mechanics Using “Different” Rules of Algebra....Pages 313-340
Variational Principles of Continuum Mechanics....Pages 341-348
Variational Principles of Continuum Mechanics....Pages 349-365
Back Matter....Pages 366-387
Content:
Front Matter....Pages i-viii
Introduction....Pages 1-2
Energy Methods, Classical Calculus of Variations Approach — Selected Topics and Applications....Pages 3-106
The Legendre Transformation, Duality and Functional Analytic Approach....Pages 107-205
Some Known Variational Principles In Elasticity....Pages 206-245
Variational Formulation of Problems of Elastic Stability. Topics in the Stability of Beams and Plates....Pages 246-312
An Example of a Variational Approach to Mechanics Using “Different” Rules of Algebra....Pages 313-340
Variational Principles of Continuum Mechanics....Pages 341-348
Variational Principles of Continuum Mechanics....Pages 349-365
Back Matter....Pages 366-387
....