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A Student's Guide to Lagrangians and Hamiltonians, by Patrick Hamill
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A concise but rigorous treatment of variational techniques, focussing primarily on Lagrangian and Hamiltonian systems, this book is ideal for physics, engineering and mathematics students. The book begins by applying Lagrange's equations to a number of mechanical systems. It introduces the concepts of generalized coordinates and generalized momentum. Following this the book turns to the calculus of variations to derive the Euler-Lagrange equations. It introduces Hamilton's principle and uses this throughout the book to derive further results. The Hamiltonian, Hamilton's equations, canonical transformations, Poisson brackets and Hamilton-Jacobi theory are considered next. The book concludes by discussing continuous Lagrangians and Hamiltonians and how they are related to field theory. Written in clear, simple language and featuring numerous worked examples and exercises to help students master the material, this book is a valuable supplement to courses in mechanics.
- Sales Rank: #187991 in Books
- Published on: 2013-12-23
- Released on: 2013-11-21
- Original language: English
- Number of items: 1
- Dimensions: 8.98" h x .39" w x 5.98" l, .70 pounds
- Binding: Paperback
- 181 pages
Review
"... in a logically clear and physically rigorous way the book highlights the landmarks of the analytical mechanics so that the attentive student can be easily prepared for the exam. It is suitable for studying in intermediate and upper-level undergraduate courses of classical mechanics ..."
Vladimir I. Pulov, Journal of Geometry and Symmetry in Physics
About the Author
Patrick Hamill is Professor Emeritus of Physics at San Jos� State University. He has taught physics for over thirty years and his research interests are in celestial mechanics and atmospheric physics.
Most helpful customer reviews
45 of 49 people found the following review helpful.
Thumbs Up for Kindle
By Let's Compare Options Preptorial
I've seen this little 180 pager going for almost 80 bucks US, so the natural two questions are:
1. Is it worth it?
2. What about Kindle?
Yes to 1, as it gives a really stripped down, very simplified intro that will help through a LOT of the more difficult aspects of the calculus of variations. The author jokes that even the most overused formulas for acceleration in physics texts use oversimplified accelerations in Cartesian planes to hide the fact that any real, generalized analytic solutions are actually all subsets of advanced Hamilton-Jacobi formulas! Other than the most basic, most motion formula problems actually require numeric rather than analytic methods.
For 2-- Great news. Although Kindle (and most e readers) slaughter LaTex, this little book on Kindle ROCKS. The publisher took the time and care to be sure the formulas and illustrations worked. Don't laugh, many do not do this! Yes, you have the minor hassle of a few e-page breaks where you have to go back and forth for an illustration, but the formulas are "blocked" so they are readable on every device I've tried, from my Android Note II to cloud/laptop and Kindle Fire. This is good news, because instead of making an $80 text $79 on Kindle like some publishers (grrrr), this sweet little text is about $13 on Kindle at this writing. Go for it!
The author recommends a LOT of other titles for the "full" story with more applications and advanced treatments-- but two to consider that are just awesome are:
Hamiltonian and Lagrangian Dynamics: Volume 1 and Hamiltonian and Lagrangian Dynamics: Volume 2.
25 of 26 people found the following review helpful.
A good reading on classical mechanics.
By ScienceThinker
Some time ago, I had written a review about Analytical Mechanics by L.N. Hand and J.D. Finch saying that, although it contains the majority of the required material for a classical mechanics course, it is badly written and there is need for a well written textbook. The current book (published by the same publisher) fills this hole. It is indeed well written. It focuses on all fundamental concepts and constructions of classical mechanics and it does so in a concise way. As a result, students will find this book extremely valuable and, most probably, it will become of their favorite books. However, researchers or other people with good knowledge of the subject will not benefit from this book at all. Hence, the preamble to the title `A Student's Guide to' is right on target.
Trying to present the most essential ideas of the topic, the author has decided to exclude all standard applications such as scattering, central potentials, rigid body, chains of particles, small oscillations, etc. Hence, it cannot be considered a standard textbook and, on its own, it cannot serve as a standalone reading on classical mechanics. In addition, the effort to suppress the size of the book has resulted in not including many examples, solved problems and a thorough end-of-chapter list of problems.
Overall, it is a really good book and students should make it part of their recommended reading. However, they should still look for additional texts which include the topics omitted in this one.
20 of 20 people found the following review helpful.
Excellent text, but detailed solutions to the problem sets similar to those provided by Fleisch would be helpful.
By Thomas J. Wilson
This is an excellent text; the perfect resource for anyone attempting to follow Leonard Susskind's Opencourseware Stanford lectures on Classical Mechanics. The text provides much of the information that Susskind either assumes you know or skims over. (The lectures are wonderful, too.) My problem with this "Student's Guide" is that, unlike Daniel Fleisch's very fine Student's Guide to Vectors and Tensors and his even better Student's Guide to Maxwell's Equations, answers to the problems are provided, but not detailed solutions to problems are not. I have followed Feynman's recommendation to his sister when she did not understand certain aspects of physics to reread the text and retry the problems until you do. Still, Fleisch provided a web site which worked you through the solutions in a very thorough fashion. As no such web site or answer book is provided for with this text I sometimes find myself feeling a little like a fish out of water. Perhaps some kind graduate student of Dr. Hamill's could provide a resource similar to Fleisch's.
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