Lagrangian and Hamiltonian Mechanics

Lagrangian and Hamiltonian Mechanics

Lagrangian and Hamiltonian Mechanics
By M. G. Calkin

Publisher: World Scientific Publishing Company
Number Of Pages: 216
Publication Date: 1996-07-04
ISBN-10 / ASIN: 9810226721
ISBN-13 / EAN: 9789810226725
Binding: Hardcover

This book takes the student from the Newtonian mechanics typically taught in the first and the second year to the areas of recent research. The discussion of topics such as invariance, Hamiltonian Jacobi theory, and action-angle variables is especially complete; the last includes a discussion of the Hannay angle, not found in other texts. The final chapter is an introduction to the dynamics of nonlinear nondissipative systems. Connections with other areas of physics which the student is likely to be studying at the same time, such as electromagnetism and quantum mechanics, are made where possible. There is thus a discussion of electromagnetic field momentum and mechanical "hidden"; momentum in the quasi-static interaction of an electric charge and a magnet. This discussion, among other things explains the "(e/c)A"; term in the canonical momentum of a charged particle in an electromagnetic field. There is also a brief introduction to path integrals and their connection with Hamilton's principle, and the relation between the Hamilton Jacobi equation of mechanics, the eikonal equation of optics, and the Schr%26ouml;dinger equation of quantum mechanics. The text contains 115 exercises. This text is suitable for a course in classical mechanics at the advanced undergraduate level.

Summary: Good and short: really good on field momentum.
Rating: 5

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.

Summary: Very Brief
Rating: 4

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.

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