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

Mark Levi

03/2014 · Student Mathematical Library Livro 69 · American Mathematical Soc.

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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.

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Mark Levi, Pennsylvania State University, University Park, PA, USA