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Classical Mechanics with Calculus of Variations and Optimal Control

An Intuitive Introduction

Mark Levi (author)

ISBN: 9780821891384

Publication Date: Mar 2014

Format: Paperback

This is an intuitively motivated presentation of many topics in classical mechanics and related areas of control theory and calculus of variations. 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 of the gyroscopic effect; a revealing equivalence between the dynamics of a particle and statics of a spring; and a short geometrical explanation of Pontryagin's Maximum Principle.
£41.50

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  • Table of Contents
  • Author Biography
  • Customer Reviews
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 zero tolerance for unrevealing 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 couple of chapters, aimed at more advanced readers, the Hamiltonian and the 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.

This book is published in cooperation with Mathematics Advanced Study Semesters.

Reviews

"This book can be recommended to students and also to everyone involved in preparing an introductory course in advanced classical mechanics, due to the well-selected material and, even more so, the clear presentation." - Zentralblatt Math

"One of the most valuable aspects of the book - unfortunately rare among textbooks - is that we see an author in command of his subject who shares not just the bare facts but how he thinks about them and how all the pieces fit together." - MAA Reviews
Pages 299
Date Published 30 Mar 2014
Publisher American Mathematical Society
Series Student Mathematical Library
Series Part 69
Subject/s Differential calculus & equations   Mathematical physics  
  • Preface
  • One degree of freedom
  • More degrees of freedom
  • Rigid body motion
  • Variational principles of mechanics
  • Classical problems of calculus of variations
  • The conditions of Legendre and Jacobi for a minimum
  • Optimal control
  • Heuristic foundations of Hamiltonian mechanics
  • Bibliography
  • Index
Mark Levi, Pennsylvania State University, University Park, PA, USA

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