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 Schrödinger equation of quantum mechanics. The text contains 115 exercises. This text is suitable for a course in classical mechanics at the advanced undergraduate level.
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I like the book because of the clear precision with which it expresses the results it eventually arrives at, the straightforward ways in which it illustrates the use of these results, and the sets of nontrivial end-chapter exercises that provide a rich opportunity to verity one s own grasp of the methods to which one is introduced in the text. --Am. J. Phys.
It is a nice and well-written book … there is a good supply of exercises and worked examples that render this little handbook a useful tool for all those who would like to learn and understand something about mechanics. --Mathematics Abstracts
It is a nice and well-written book … there is a good supply of exercises and worked examples that render this little handbook a useful tool for all those who would like to learn and understand something about mechanics. --Mathematics Abstracts
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Most Helpful Customer Reviews
35 of 39 people found the following review helpful:
5.0 out of 5 stars
Good and short: really good on field momentum.,
By pdel (Ireland) - See all my reviews
This review is from: Lagrangian and Hamiltonian Mechanics (Hardcover)
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.
32 of 36 people found the following review helpful:
4.0 out of 5 stars
Very Brief,
By A Customer
This review is from: Lagrangian and Hamiltonian Mechanics (Hardcover)
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.
9 of 9 people found the following review helpful:
5.0 out of 5 stars
Excellent Preparation for Graduate Level Mechanics,
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This review is from: Lagrangian and Hamiltonian Mechanics (Hardcover)
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!
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