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Classical Mechanics with Calculus of Variations and Optimal Control: An Intuitive Introduction
Mark Levi
Price
1160.00
ISBN
9781470425982
Language
English
Pages
300
Format
Paperback
Dimensions
140 x 216 mm
Year of Publishing
2016
Territorial Rights
Restricted
Imprint
Universities Press

This is an intuitively motivated presentation of many topics in classical mechanics and related areas of control theory and calculus of variations. All topics throughout the book are treated with tolerance for unraveling definitions and for proofs which leave the reader in the dark. Some areas of particular interest are an extremely short derivation of the ellipticity of planetary orbits; a statement and an explanation of the ‘tennis racket paradox’; a heuristic explanation (and a rigorous treatment) of the gyroscopic effect; a revealing equivalence between the dynamics of a particle and statics of a spring; a short geometrical explanation of Pontryagin’s maximum principle, and more. In the last chapter, aimed at more advanced readers, the Hamiltonian and momentum are compared to forces in a certain static problem. This gives a palpable physical meaning to some seemingly abstract concepts and theorems. With minimal prerequisites consisting of basic calculus and basic undergraduate physics, this book is suitable for courses from an undergraduate to a beginning graduate level, and for a mixed audience of mathematics, physics and engineering students. Much of the enjoyment of the subject lies in solving almost 200 problems in this book.

Mark Levi is Professor of Mathematics at Pennsylvania State University, University Park, USA.

Series Foreword: MASS and REU at Penn State University 
Preface 
Chapter 1. One Degree of Freedom 
Chapter 2. More Degrees of Freedom 
Chapter 3. Rigid Body Motion 
Chapter 4. Variational Principles of Mechanics 
Chapter 5. Classical Problems of Calculus of Variations 
Chapter 6 The Conditions of Legendre and Jacobi for a Minimum 
Chapter 7. Optimal Control 
Chapter 8. Heuristic Foundations of Hamiltonian Mechanics 
Bibliography
Index

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