**Student Mathematical Library**

Volume: 69;
2014;
299 pp;
Softcover

MSC: Primary 34; 37; 49; 70; 00;

Print ISBN: 978-0-8218-9138-4

Product Code: STML/69

List Price: $42.00

Individual Price: $33.60

**Electronic ISBN: 978-1-4704-1444-3
Product Code: STML/69.E**

List Price: $42.00

Individual Price: $33.60

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#### Supplemental Materials

# Classical Mechanics with Calculus of Variations and Optimal Control: An Intuitive Introduction

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*Mark Levi*

It is hard to imagine a more original and insightful approach to classical mechanics. Most physicists would regard this as a well-worn and settled subject. But Mark Levi's treatment sparkles with freshness in the many examples he treats and his unexpected analogies, as well as the new approach he brings to the principles. This is inspired pedagogy at the highest level.

—Michael Berry, Bristol University, UK

How do you write a textbook on classical mechanics that is fun to learn from? Mark Levi shows us the way with his new book: “Classical Mechanics with Calculus of Variations and Optimal Control: An Intuitive Introduction.” The combination of his unique point of view with his physical and geometrical insights and numerous instructive examples, figures and problem sets make it a pleasure to work through.

—Paul Rabinowitz, University of Wisconsin

This is a refreshingly low key, down-to-earth account of the basic ideas in Euler-Lagrange and Hamilton-Jacobi theory and of the basic mathematical tools that relate these two theories. By emphasizing the ideas involved and relegating to the margins complicated computations and messy formulas, he has written a textbook on an ostensibly graduate level subject that second and third year undergraduates will find tremendously inspiring.

—Victor Guillemin, MIT

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 chapter, 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

#### Readership

Undergraduate and graduate students interested in classical mechanics and ordinary differential equations.

#### Reviews & Endorsements

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

#### Table of Contents

# Table of Contents

## Classical Mechanics with Calculus of Variations and Optimal Control: An Intuitive Introduction

- Cover Cover11 free
- Title page iii4 free
- Foreword v6 free
- Contents vii8 free
- Preface xiii14 free
- One degree of freedom 122 free
- More degrees of freedom 7596
- Rigid body motion 141162
- Variational principles of mechanics 167188
- Classical problems of calculus of variations 183204
- The conditions of Legendre and Jacobi for a minimum 211232
- Optimal control 233254
- Heuristic foundations of Hamiltonian mechanics 257278
- Bibliography 295316
- Index 297318 free
- Back Cover Back Cover1322