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Hamiltonian and Lagrangian Dynamics: Volume 2, by James Curry
Download PDF Hamiltonian and Lagrangian Dynamics: Volume 2, by James Curry
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Hamiltonian and Lagrangian Dynamics is useful for solving difficult mechanics problems, and is critical for understanding Quantum Mechanics and Quantum Field Theory. The present text is unique for its emphasis on geometric reasoning and intuition, and for its accessibility. Volume 1 is primarily mathematical, covering Linear and Abstract Algebra, Functional Analysis and Differential Geometry, and Volume 2 is primarily devoted to physics, beginning with a serious approach to Newtonian physics, then Hamiltonian and Lagrangian Dynamics, including classical field theory, the basis of Quantum Field theory. This book is intended to be used by physics undergraduates who have just finished the Calculus sequence and by physics graduate students. Beginning mathematics students will also find it useful, for introducing some modern mathematics in a way that is accessible, and then showing some of its many uses. Engineering students may also be interested in this book.
- Sales Rank: #1626763 in Books
- Published on: 2013-11-02
- Original language: English
- Dimensions: 11.00" h x .93" w x 8.50" l, 2.10 pounds
- Binding: Paperback
- 412 pages
Most helpful customer reviews
9 of 9 people found the following review helpful.
Undiscovered Gem Too Narrowly Titled
By Let's Compare Options Preptorial
This amazing two volume series of advanced mathematics represents over 700 pages of state of the art math with applications in physics, engineering and dynamical systems in general, as well as numerous advanced dynamics topics for math track students.
The book is mis-titled as Hamiltonians and Lagrangians, because although it has some of the best and most up to date coverage of those areas, it contains FAR MORE "math for dynamics" (including physics and engineering) in "leading up" to the very thorough, accurate and up to date Hamiltonian and Lagrangian topics. As an example, the first volume starts at basic linear algebra and calc, and leads all the way up to manifolds, projective geometry and kinematics.
The other "mis-title" aspect is the quality of the instruction. This is subtle. When you read the current title, you might assume this is a densely packed set of tomes on formula after formula with proofs and derivations fit only for graduate physicists or mathematicians. Instead, the two texts contain some of the best pure TEACHING of ANY math book I've reviewed or used for my online dynamics classes. Curry takes a "geometric" approach, taking the time and space to explain in words, formulas AND pictures, the point of higher math applications.
Even better, the author has a genuinely deep intuitive grasp of what's "really going on" with vectors. He uses this understanding as a "theme" for both texts, which gives readers a one of a kind feel for ALL advanced math through that frame. Even the toughest problems and examples hearken back to "Why isn't this like the vectors we've studied?" and "How does looking at this from the point of view of a vector or matrix allow us to manipulate the coordinate axes more easily?" By then augmenting those insights and intuitive benefits geometrically, the books are PACKED with "aha" moments even for advanced engineering, math and physics students and teachers.
Even though this is a CreateSpace title, which can vary in quality, the texts are of extremely high quality and the author didn't skimp on any details. The paper is thick, allowing copious notes and highlighting without bleeds, and the texts are large, with plenty of room for margin marking and your own callouts for the copious illustrations.
The material is intended for undergrad up, but bright AP High School students can gain a lot from the orientation chapters. I NEVER recommend too advanced work if it is too tough (and Hamiltonians are tough, as the Swiss Army Knife of nearly all of Physics today), but the author clearly had autodidacts and engineering/ physics types like me in mind in including as much intuitive and geometric material as he does.
Dynamics teachers use four "channels" for different types of problems-- analytic, qualitative, numeric and stochastic. Analytic are formulas, qualitative are geometric and graphic, numeric are algorithmic starting with "seed" guesses, and stochastic, the newest member of the family, are mostly research applications where combinatorics get so hairy they are handled as random or chaotic. (Even some oscillators like pendulums are nonlinear because they have a sin function, or when they "loop over" the top of the pendulum when enough force is applied. How much? That's where they become nonlinear!).
We didn't learn a lot of this in EE school, but dynamics (especially ordinary differential equations) abound in circuits, and EEs are gradually warming to Hamiltonians. This is a GREAT place for catch up it that's you! By the way, the four channels aren't just for learning, they also are "required" by the problem design itself, because some problems, especially things like higher N bodies, nonlinear, etc. just CANNOT be solved with formulas. Where the PDE or ODE is "understood" however, Hamiltonians, Lagrangians, Fouriers, etc. can give a "pseudo" linear look that can then be intuitively solved, or at least, as we engineers would say, get "close enough!"
Highly recommended series. One of the few I'd recommend buying on your own even if not required for a class, and certainly for self study. It will fill in a LOT of gaps in really "getting" what's hidden in those cryptic proofs and far too brief (1.3.27) type formula statements! Frankly, geometry rocks, and this is one of the few authors that really gets it, and takes the time to show us with concern for his readers. Handholding abounds-- not something you can say with many texts today! Takes a special writer to avoid "showing off" -- this is a true teacher who cares about his readers' grasp of the material from many perspectives.
0 of 1 people found the following review helpful.
Five Stars
By Jonathan R. Grimm
Excellent, comprehensive coverage of the subject with excellent supplementation of essential mathematics. Fonts are just fine.
3 of 8 people found the following review helpful.
Terrible book on Hamiltonian mechanics......
By Nicholas E. Davis
Pretty poorly written book on Hamiltonian equations as well as Lagrangian mechanics.....Even the type seemed skewed in some areas...somewhat pixelated and blurry in some parts...especially when noting formulas....the print was very poorly done....
I will say that it had quite an extensive review on the basics of Newtonian Physics: torque, force incline, Conservation of Energy problems, etc.....However, most of the book scarcely covered Hamiltonians, and that was the primary reason why I purchased the book in the first place....Use this to supplement your coursework....Good for a quick review, but...other than that...you shouldn't bother spending a huge amount of time on this book....
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