An Introduction to Modern Variational Techniques in Mechanics and Engineering

This book is devoted to the basic variational principles of mechanics, namely the Lagrange--D’Alembert differential variational principle and the Hamilton integral variational principle. These two variational principles form the basis of contemporary analytical mechanics, and from them the body of classical dynamics can be deductively derived as a part of physical theory. In recent years variational techniques have evolved as powerful tools for the study of linear and nonlinear problems in conservative and nonconservative dynamical systems, as is emphasized in this book. Presented here are a wide range of possibilities for applying variational principles to numerous problems in analytical mechanics, including the Noether Theorem for finding conservation laws of conservative and nonconservative dynamical systems, the application of the Hamilton--Jacobi and field methods suitable for nonconservative dynamical systems, the variational approach to modern optimal control theory, and the application of variational methods to the stability and optimization of elastic rod theory. Mathematical prerequisites are kept to a minimum, and the exposition is intended to be suggestive rather than mathematically rigorous. Each chapter begins with widely understood mathematical principles and unfolds systematically toward more advanced topics. Examples and novel applications are presented throughout to clarify and enhance the theory. An Introduction to Modern Variational Techniques in Mechanics and Engineering will serve a broad audience of students, researchers, and professionals in analytical mechanics, applied variational calculus, optimal control, physics, and mechanical and aerospace engineering. The book may be used in graduate and senior undergraduate dynamics courses in engineering, applied mathematics, and physics departments, or it may also serve as a self-study reference text.