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. Many 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. This book reflects the strong connection between calculus of variations and the applications for which variational methods form the fundamental foundation. 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. The majority of the text consists of applications of variational calculus for a variety of fields.
A graduate of Lehigh University and former National Research Council Postdoctoral Fellow at the National Institute of Standards and Technology, Kevin W. Cassel is Associate Professor of Mechanical and Aerospace Engineering at the Illinois Institute of Technology (IIT). He has been a visiting researcher at the University of Manchester and University College London, and is a visiting professor at the University of Palermo, Italy. Professor Cassel's research utilizes computational fluid dynamics in conjunction with advanced analytical methods to address problems in bio-fluids, unsteady aerodynamics, multiphase flow, and cryogenic fluid flow and heat transfer. Dr Cassel is an Associate Fellow of the American Institute of Aeronautics and Astronautics, and his honors include IIT's University Excellence in Teaching Award (2008) and Ralph L. Barnett Excellence in Teaching Award (2007, 2001), the 2002 Alfred Noble Prize, and the Army Research Office Young Investigator Award (1998-2001).
1. Preliminaries; 2. Calculus of variations; 3. Rayleigh-Ritz, Galerkin, and finite-element methods; 4. Hamilton's principle; 5. Classical mechanics; 6. Stability of dynamical systems; 7. Optics and electromagnetics; 8. Modern physics; 9. Fluid mechanics; 10. Optimization and control; 11. Image processing and data analysis; 12. Numerical grid generation.