Classical Mechanics With Calculus of Variations and Optimal Control: An Intuitive Introduction (Student Mathematical Library)

by Mark Levi

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 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.

Genres: Mathematics, Science, Physics

299 pages, Paperback

First published December 1, 2013

About the author

Librarian Note: There is more than one author in the Goodreads database with this name.

This is 1^ Mark Levi

2^Mark Levi - Serbian for Marc Levy
3^Mark Levi - Photographer
4^Mark Levi - Cook book

Reviews

[Stephen · Rating 3 out of 5]

I found many typos in this book which really added to the confusion due to parameters and variables introduced seemingly at random. So, this book starts off very well but then quickly becomes mired in proofs where the typos really become a hindrance unless you know the argument beforehand. Not recommended.

[Shaun Zhang · Rating 3 out of 5]

This book has many good examples and exercises. And it emphasizes the intuition behind the mechanism of force, which I think is pretty interesting. For example, the author make a complete correspondence between particle dynamics with statics of spring. It is readable and good for very beginner.