This book is devoted to the basic variational principles of
mechanics, namely the Lagrange--Da (TM)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
aerospaceengineering. 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.
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