VARIATIONAL METHODS WITH APPLICATIONS IN SCIENCE AND ENGINEERING

There is a resurgence of applications in which the calculus of variations has direct relevance. In addition to application to solid mechanics and dynamics, it is now being applied in a variety of numerical methods, numerical grid generation, modern physics, various optimization settings, and fluid dynamics, for example. Many of these applications, such as nonlinear optimal control theory applied to continuous systems, have only recently become tractable computationally, with the advent of advanced algorithms and large computer systems. The content of the text reflects the strong connection between calculus of variations and the applications for which variational methods form the fundamental foundation. Most readers will be pleased to note that the mathematical fundamentals of calculus of variations (at least those necessary to pursue applications) is rather compact and is contained in a single chapter of the book. Therefore, the majority of the text consists of applications of variational calculus for a variety of fields. - Emphasis on modern applications - Provides a concise treatment of the calculus of variations - Derivation of the ubiquitous Hamilton''s principle directly from the first law of thermodynamics - Includes derivation of the governing equations of many discrete and continuous phenomena from Hamilton''s principle