Customer Reviews

Lagrangian and Hamiltonian Mechanics

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I read physics books in my spare time, and what I've found are the best ones are short, good books: if they're short you stand a chance of getting through them, and then if they're good you can pick up the essentials of the subject quickly.

This book is both. If you're looking for a primary textbook, you might be looking for something different, but for a reference to the concepts it's short and sweet: eg. what are canonical transformations, why are they defined the way they are and what is their importance.

What's particularly mind-blowing is the 5 page discussion of field momentum. That's the qA term in the hamiltonian for a charge q in a magnetic field (vector potential A). This form of the hamiltonian always puzzled me: Calkin explains the meaning of the qA term beautifully. The book is worth getting for this alone.

We are using this book in a third-year undergraduate course in classical mechanics. I find it alright for an in-class course, but I would definetely not recommend it to anyone planning to study by him/herself. The text simply is not made for that.
Judging by what I see in other books, this text has a fairly thorough coverage.
It is written VERY short and you want to have a pen and paper ready to understand the analysis. Once you do that, it should be alright.
The problems are of the very-short-but-sometimes-algebraically-intense kind, the class record being at 52 (!) hand written pages for three problems in chapter 6. But they are possible and, aside from the algrebra, not all that difficult.

Since Amazon doesn't have "See Inside" activated for this book, here is a quick rundown of its table of contents:

Chapter 1 - Newton's Laws

Newton's Laws
Free fall
Simple harmonic oscillator
Central force
Gravitational force: qualitative
Gravitational force: quantitative
Parameters of earth's orbit
Scattering
Coulomb scattering
Exercises


Chapter 2 - The Principle of Virtual Work and D'Alembert's Principle

Constraints
Principle of virtual work
D'Alembert's principle and generalized coordinates
Lever
Inclined plane
Plane pendulum
Exercises


Chapter 3 - Lagrange's Equations

Lagrange's Equations
Plane pendulum
Spherical pendulum
Electromagnetic interaction
Interaction of an electric charge and a magnet
Exercises


Chapter 4 - The Principle of Stationary Action or Hamilton's Principle

Principle of stationary action
Calculus of variations
Geodesics
Examples
Path integral formulation of quantum mechanics
Exercises


Chapter 5 - Invariance Transformations and Constants of the Motion

Invariance Transformations
Free particle (a)
Infinitesimal transformations
Free particle (b)
Space time transformations
Spatial displacement
Spatial rotation
Galilean transformation
Time displacement
Covariance, invariance, and the action
Exercises


Chapter 6 - Hamilton's Equations

Hamilton's equations
Plane pendulum
Spherical pendulum
Rotating pendulum
Electromagnetic interaction
Poisson brackets
Exercises


Chapter 7 - Canonical Transformations

One degree of freedom
Generating functions
Identity and point transformations
Infinitesimal canonical transformations
Invariance transformations
Lagrange and Poisson brackets
Time dependence
Integral invariants
Exercises


Chapter 8 - Hamilton-Jacobi Theory

Hamilton's principal function
Jacobi's complete integral
Time-independent Hamilton-Jacobi equation
Separation of variables
Free particle, in cartesian coordinates
Central force, in spherical coordinates
Hamilton-Jacobi mechanics, geometric optics, and wave mechanics
Exercises


Chapter 9 - Action-Angle Variables

Action-angles variables
Example: simple harmonic oscillator
Example: central force
Adiabatic change
Exercises


Chapter 10 - Non-Integrable Systems

Surface of section
Integrable and non-integrable systems
Perturbation theory
Irrational tori
Rational tori
Exercises


Index


The exposition is of high quality throughout and is supplemented by over 80 figures. In addition, the exercises are excellent and form an essential part of the text, although they tend to be algebraically laborious. I would recommend that anyone using this book for self study also acquire Lagrangian and Hamiltonian Mechanics: Solutions to the Exercises as this book often provides efficient tricks for solving these types of problems that are good to know.

One of the outstanding features of this book are some of its supplementary discussions such as the one on the Electromagnetic Field and field momentum in chapter three, the discussion of time dilation in general relativity and the path integral formulation of quantum mechanics in chapter four, the connections between Hamilton-Jacobi mechanics, geometrical optics and quantum mechanics in chapter 8, and essentially all of chapter 10.

A few of the things I didn't care for were the occasional shady handling of infinitesimals and differential forms, and the odd omission of any mention of chaos in chapter 10.

Regardless though, diligent study of this book will definitely bring your classical mechanics up to the level where it needs to be for grad school.

Enjoy!