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Lagrangian and Hamiltonian Mechanics, by M. G. Calkin
Download Ebook Lagrangian and Hamiltonian Mechanics, by M. G. Calkin
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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.
- Sales Rank: #1368643 in Books
- Brand: Calkin, M. G.
- Published on: 1996-07-04
- Original language: English
- Number of items: 1
- Dimensions: 8.60" h x .80" w x 6.10" l, 1.03 pounds
- Binding: Hardcover
- 216 pages
Review
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
Most helpful customer reviews
26 of 27 people found the following review helpful.
Excellent Preparation for Graduate Level Mechanics
By Jason Dowd
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!
36 of 40 people found the following review helpful.
Very Brief
By A Customer
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.
38 of 43 people found the following review helpful.
Good and short: really good on field momentum.
By pdel
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.
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