Mathematical Methods of Classical Mechanics (Graduate Texts in Mathematics)

Book Description

In this text, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism. This modern approch, based on the theory of the geometry of manifolds, distinguishes iteself from the traditional approach of standard textbooks. Geometrical considerations are emphasized throughout and include phase spaces and flows, vector fields, and Lie groups. The work includes a detailed discussion of qualitative methods of the theory of dynamical systems and of asymptotic methods like perturbation techniques, averaging, and adiabatic invariance.

Customer Reviews:

A unique, masterful and enjoyable book for graduate student in physics.......2007-02-08

The book is full of little enjoyable details (jewels). Arnold is one of the few mathematicians which approaches problems with a very geometric point of view. In his interview with S.H. Lui he mentions how algebraic picture has dominated the research in mathematics and how he has tried to counter that. One can see the trace of his ingenuity all over this book. What some may call as handwaving in math circles is indeed called as physical (or geometric) intuition in physics community and is being actively encouraged.

The chapters on oscillations (chap. 5) and perturbation theory (chap. 10) are very instructive. For example, parametric resonance is discussed concisely in chapter 5 which you won't be able to find it anywhere else. where can you learn about "Arnold's tongues" better than in Arnold's book?

There are so many appendices at the end of the book. They are often very specialized and I don't recommend you to read them on your first read.

In conclusion, I recommend this book to any physics graduate student. In fact, I hope one day it will be used as a text book for courses in classical mechanics.

I would recommend foundations of mechanics by Marsden.......2006-01-07

I have to admit that I haven't thoroughly read through this text. But judging from the first 10 pages, there is a lot of mathematical handwaving. In contrast, foundations of mechanics (hereafter FOM) is far superior in that it provides all the necessary background beyond calculus and linear algebra to the reader, and is logically consistent so far in my reading. I want to mention that there are certainly complete and excellent texts out there on functional analysis, differential geometry, and topology, but many texts include way more stuff than you would want to know. In particular, it is my humble opinion that once you get to a certain point of knowledgeability of a subject like algebraic topology, you have enough of a taste for it that to learn more of the subject would only help if you were to go into research. Therefore a book like FOM provides a concise and practical treatment of those various advanced mathematics topics.

Best book on CM.......2004-02-26

Best book on CM (based most on symplectic formulation). Extremely clear if one has enough patience to follow exactly the author's way and to work out the proposed stimulating problems. Contains an original way of introducing differential forms, integration of differential forms and homology/De Rahm's thm.: you fully get in the subject in few pages ! The first part does not make use of symplectic formalism but is also quite original and stimulating. The level is last yr. undergr. 1st yr. graduate. Very useful if used with E. ott (Chaos in Dynamical Systems) for studying nonlinear dynamics.

Encyclopedic.......2002-05-08

Extremely stimulating, uses Galileo to motivate Newton's laws instead of postulating them. Treatment of Bertrand's theorem is beautiful, but contains one error (took me 2 years before I realized where..). However, I know of only one physicist who successully worked out all the missing steps and taught from this book. I know mathematicians who have cursed it. I used/use it for inspiration. The treatment of Liouville's integrability theorem, I found too abstract, found the old version in Whittaker's Analytical Dynamics to be clearer (Arnol'd might laugh sarcastically at this claim!)--for an interesting variation, but more from the standpoint of continuous groups, see the treatment in ch. 16 of my Classical Mechanics (Cambridge, 1997). In my text I do not restrict the discussion of integrability/nonintegrability to Hamiltonian systems but include driven dissipative systems as well. Another strength of Arnol'd: his discussion of caustics, useful for the study of galaxy formation (as I later learned while doing work in cosmology). Also, I learned from Arnol'd that Poisson brackets are not restricted to canonical systems (see also my ch. 15). I guess that every researcher in nonlinear dynamics should study Arnol'd's books, he's the 'alte Hasse' in the field.

The best, but challenging for not-mathematicians.......2001-10-21

Arnold shines for clarity, completeness and rigour. But, at the same time, he requires a remarkable intellectual effort on the part of the reader (at least a physicist or an engineer). Some readers might see this as a book of math rather than physics, but that would not be fair: Arnold always stresses the geometrical meaning and the physical intuition of what he states or demonstrates. You can take full advantage from the effort of reading this book only if you master a wide range of mathematical topics: essentially differential geometry, ODEs and PDEs and some topology. That's not always true for engineer or physics students at the beginning graduate level. For that kind of readers, Goldstein is a much better fit. Arnold can (and maybe should) be read afterwards.
On the other hand, the exercises, although not very numberous, are very well conceived and help a lot to deepen the comprehension of the text. Also, the order of the topics is linear and very effective from a didactic point of view. The exposition is clear, concise and always goes straight to the point. Thanks to these features, it is one of the most effective books for self-teaching I ever happened to read.
From a physical point of view, the domain of applications is essentially limited to discrete systems. Furthermore, the electromagnetism and relativity are not even cited, although they can be viewed as the logical completion of classical mechanics (see, for example, Goldstein). But the extreme generality of the approach largely balance the more restricted physical domain. In my opinion, the best book you can read on the topics.

Nonlinear Interactions: Analytical, Computational, and Experimental Methods

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Nonlinear Interactions: Analytical, Computational, and Experimental Methods
Ali H. Nayfeh
Manufacturer: Wiley-Interscience
ProductGroup: Book
Binding: Hardcover

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ASIN: 0471175919

Book Description

Nonlinear Interactions provides a coherent and unified treatment of analytical, computational, and experimental methods and concepts of modal interactions. This book is an obvious extension of Ali Nayfeh's well-known book Applied Nonlinear Dynamics (with Bala Balachandran). These methods are used to explore and unfold in a unified manner the fascinating complexities in nonlinear dynamical systems. The systems discussed are drawn from fluid mechanics and structural dynamics.

Nonlinear interactions between high-frequency and low-frequency modes are of great practical importance. Through the mechanisms discussed in this book, energy from high-frequency sources can be transferred to the low-frequency modes of supporting structures and foundations, and the result can be harmful large-amplitude oscillations that decrease their fatigue lives. On the other hand, these mechanisms can be exploited to transfer the energy from a system to a sacrificial subsystem and hence decrease considerably the vibrations of the main system and increase its fatigue life.

Fundamentals of Computational Fluid Dynamics (Scientific Computation)

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An easy presentation to not so easy concepts!
Fundamentals of Computational Fluid Dynamics

Fundamentals of Computational Fluid Dynamics (Scientific Computation)
H. Lomax , Thomas H. Pulliam , and David W. Zingg
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 3540416072

Book Description

This book is intended as a textbook for a first course in computational fluid dynamics and will be of interest to researchers and practitioners as well. It emphasizes fundamental concepts in developing, analyzing, and understanding numerical methods for the partial differential equations governing the physics of fluid flow. The linear convection and diffusion equations are used to illustrate concepts throughout. The chosen approach, in which the partial differential equations are reduced to ordinary differential equations, and finally to difference equations, gives the book its distinctiveness and provides a sound basis for a deep understanding of the fundamental concepts in computational fluid dynamics.

Customer Reviews:

An easy presentation to not so easy concepts!.......2007-08-23

This book presents some fundamentals of CFD based on straightforward mathematical tools giving fast access to very interesting general behaviours of PDE families. Apart from the introduction of basic concepts, finite differences and finite volume discretizations, the heart of the book lies in chapters 4,6,7 where a clear and systematic methodology to go from PDE to ODE to O(delta)E is presented. The classical stabilities associated to the most famous time steppings are presented. Some other features such as multigrid, splitting, and upwind dissipations are presented in the same clear setting. The book is very well written, clear and straightforward. I hope more advanced topics will be also included in further editions!

Fundamentals of Computational Fluid Dynamics.......2001-07-09

Fundamentals of Computational Fluid Dynamics is one of several technically useful books on the subject. What sets it apart, however, is its ability to attract and maintain the reader's interest in what could otherwise be a dry topic.

Book Description

Vladimir Krainov has produced one of the few books in the field to concentrate on qualitative methods. He presents order of magnitude solutions for physical quantities in various nonequilibrium statistical processes as well as qualitative solutions of differential equations for macroscopic nonequilibrium processes in gases and other media. Covers topics including free convection, turbulence phenomena, sound propagation, and surface phenomena.

Computational Methods for Fluid Dynamics

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Only great for complete novices
Excellent teaching book
One of the best books for CFD code developers
I give it 5 stars
A lot of excellent detail

Computational Methods for Fluid Dynamics
Joel H. Ferziger , and Milovan Peric
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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Accessories:

ASIN: 3540420746

Book Description

In its 3rd revised and extended edition the book offers an overview of the techniques used to solve problems in fluid mechanics on computers and describes in detail those most often used in practice. Included are advanced methods in computational fluid dynamics, like direct and large-eddy simulation of turbulence, multigrid methods, parallel computing, moving grids, structured, block-structured and unstructured boundary-fitted grids, free surface flows. The 3rd edition contains a new section dealing with grid quality and an extended description of discretization methods. The book shows common roots and basic principles for many different methods. The book also contains a great deal of practical advice for code developers and users; it is designed to be equally useful to beginners and experts.The issues of numerical accuracy, estimation and reduction of numerical errors are dealt with in detail, with many examples.

Customer Reviews:

Only great for complete novices.......2002-01-29

Peric's PhD thesis is one of my most precious possessions. I consider Ferziger to be one of THE greats in Large Eddy Simulation. So I had great hopes for this book. I was warned before I saw it that it contained nothing that I wouldn't already know, but even so it was a big disappointment. I could have written a better book myself and I don't have half the brain of either of the authors. I've looked at it three times and each time turned away in disgust.

This book will point a novice in the correct direction, unlike Roach's book, and unlike Patankar's in a post Rhie-Chow age, but it avoids like the plague any subject with even the slightest whiff of controversy. As any new technique is always controversial, the book was some 5 to 10 years out of date even before it hit the press. Further, it discusses each subject in a very superficial way. More depth is needed.

I want a book that will tell me what the advantages are and how to program the conjugate gradient method, algebraic multigrid, superbee, wall reflection terms for Reynolds Stress, multiphase flow, viscoelasticity, coalescence, the axis in cylindrical coordinates, grid generation, surface tension, adaptive grids, spectral elements etc. This book is no help with any of these.

I frequently get asked "What's a good book for Computational Fluid Dynamics?". I have to admit that there isn't one. The best that I know are the user manuals for the various commercial CFD packages.

To summarise, if programming CFD is a 100 step journey then this book will only take you the first 3 steps, but at least they're 3 steps in the right direction. After you've been programming CFD for a year you can probably toss the book out without any great loss.

Excellent teaching book.......2001-07-10

I found this book an excellent support in teaching and invaluable as an occasional reference in my practical work in industry. It is particularly gratifying to see that free surface flows are covered well. Best book I have seen so far in the field.

One of the best books for CFD code developers.......2001-05-24

This is the best book on CFD I' ve read. It is more useful to those who want to develop their own codes rather than CFD users: It mostly describes in deep detail (although in a concise manner) a single method used by the authors and developed by themselves and their colleagues. It is not intended to be a list of the vast number of CFD techniques developed so far.

Their method is state-of-the-art and they provide plenty of results to support it's quality. It is mostly directed towards incompressible flows. They provide a chapter that extends their method to compressible flows but they do not describe any special convection schemes for flows with shock waves. It can be applied to both structured and arbitrarily unstructured grids, although their approach to the discretization of the convection and diffusion terms is particularly useful in the case of arbitrarily unstrucured grids. State of the art subjects such as multigrid and error-driven grid refinement are also covered and integrated into their method.

I agree with a previous reviewer that they provide a very good coverage of solution methods for linear equation systems which arise in CFD. Most other books on CFD (all the ones that I have read) have a poor coverage of the subject and describe only old and inneficient methods. However even this book does not sufficiently describe conjugate-gradient type methods or Krylov subspace methods in general, but references are provided.

In conclusion, this book is not for beginners but for code developers who have some basic knowlwdge of CFD and a relatively good mathematical background.

I give it 5 stars.......2001-03-16

I agree with the reviewer that said this book is complimentary to an intro text such as Patankar. This is not a cook book for a first time coder. But it is a really great reference for the Finite Volume dilettante.

I really appreciate that all numerical results presented are thoroughly documented. That counts.

Really, really nice chapter on iterative solvers....

Good overall description on many other topics such as multi-grid methods, turbulence, grid geometry and PV coupling.

This book really helped me speed up my homegrown quite a bit.

They also have all kinds of stuff available by ftp....

A lot of excellent detail.......1998-12-22

This is a very good book for learning the details of implementing the Finite Volume method in Computational Fluid Dynamics. I view it as very complimentary to S. V. Patankar's book, which is more general in nature. Both books are geared toward people who want to write computer programs to solve fluid transport problems (heat transfer, Navier-Stokes, etc.) Both tend to focus on numerical issues (as opposed to the physics of transport phenomena). But while Pantankar's book provides a very easy, approachable introduction that is thin on the details, Ferziger & Peric have written a book rich in details. For instance, they devote an entire chapter to solving linear systems of equations. They compare all of the commonly used methods and contrast their rates of convergence for various test cases. This level of detail is great if you already understand the big picture. I think it may be somewhat difficult for someone new to CFD to really understand the finite volume method from this book alone. I would recommend Patankar's book for a good intro and this book for the implementation details.

Course of Theoretical Physics : Mechanics (Course of Theoretical Physics)

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Provides a new perspective on common concepts.
Excellent
Great book
Not Useful for Learning
Well

Course of Theoretical Physics : Mechanics (Course of Theoretical Physics)
E M Lifshitz , and L D Landau
Manufacturer: Butterworth-Heinemann
ProductGroup: Book
Binding: Paperback

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ASIN: 0750628960

Book Description

Devoted to the foundation of mechanics, namely classical Newtonian mechanics, the subject is based mainly on Galileo's principle of relativity and Hamilton's principle of least action. The exposition is simple and leads to the most complete direct means of solving problems in mechanics.

The final sections on adiabatic invariants have been revised and augmented. In addition a short biography of L D Landau has been inserted.

Customer Reviews:

Provides a new perspective on common concepts........2007-09-02

Like the title says this book provides a new perspective that allows very commonly defined quantities to arise naturally. However, this is the translation from Landau's work so the original texts are much thicker and I am sure much is lost in the translation. This is also a graduate or higher text and it difficult to follow at times but the more ways you can understand something the better.

Excellent.......2007-01-12

This book was recommended as a supplimentary text for our mechanics course. This book is 100% better than any other mechanics book I've looked at. The explanations are very clear, especially for non-inertial & rotational reference frames and the derevations for conservation of energy, momenta, and angular momenta (integrals of motion).

Includes extensive section on Euler angle derivation and tops. The examples in this text are quite difficult (more difficult than your typical undergraduate text), but they are all solved with partial work, so they are still helpful for studying.

Overall a clearly written text with good examples and excellent derivations.

Great book.......2007-01-09

It is wonderful book to learn the basics of mechanics. It will be best for the people who start to take fundamental physics course in college.

Not Useful for Learning.......2006-12-02

Way overrated. L&L lacks motivation and empiricism. Justifications behind their derivations are often specious. If you know the subject, it's a nice perspective. Otherwise, it's useless. Two stars, instead of zero, for their oustanding elegance. Based on previous raves, have read now V.1 and V.2 of their course of physics. Doubt that i will waste time on other volumes.

Well.......2006-06-20

Having lived in eastern europe all my life where textbooks are more or less just like Landau's I have to say that I by far prefer the American ones, many times more expensive though they may be. This book is outdated, as it only treats integrable systems, and utterly unsuitable for learning mechanics from, though it makes an excellent review of the theory if you have already learned it from another book.

If there was nothing else to remark I would have given it three stars based on this, but the book looks like it's photocopied from the original typewritter transcript. The book (mine being a 2005 reprint) has terrible printing quality. The paper and binding look like they are the cheapest the publisher could get. If this were an estern european textbook it would be sold for $5. To top it off, my copy came with a very strange folding defect.

These defects were shared by all three of Landau's books I ordered. Needless to say, I shan't be getting the rest of them. Instead I recommend getting a newer text such as the excellent _Structure and Intepretation of Classical Mechanics_ or somesuch, and I recommend that Americans stop seeing gold in everything that's foreign.

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Analytic Methods in Physics
Charlie Harper
Manufacturer: Wiley-VCH
ProductGroup: Book
Binding: Hardcover

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ASIN: 3527402160

Book Description

This book presents a self-contained treatment of invaluable analytic methods in mathematical physics. It is designed for undergraduate students and it contains more than enough material for a two semester (or three quarter) course in mathematical methods of physics. With the appropriate selection of material, one may use the book for a one semester or a one quarter course. The prerequisites or corequisites are general physics, analytic mechanics, modern physics, and a working knowledge of differential an integral calculus.

Computational Transport Phenomena: Numerical Methods for the Solution of Transport Problems

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The best book I've ever read
The essential work in this field.

Computational Transport Phenomena: Numerical Methods for the Solution of Transport Problems
W. E. Schiesser , and C. A. Silebi
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Hardcover

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Transport Phenomena

ASIN: 0521553784

Book Description

Computational techniques have become indispensable tools in solving complex problems in transport phenomena. This book provides a clear, user-oriented introduction to the subject of computational transport phenomena. Each self-contained chapter includes a detailed worked example and a discussion of the problem system equations. Also included are the numerical methods used; computer code for the solution of the problem system equations; discussion of the numerical solution with emphasis on physical interpretation; and, when appropriate, a comparison of the numerical solution with an analytical solution or a discussion of how the numerical solution goes beyond what can be done analytically, especially for nonlinear problems. Intended for students and a broad range of scientists and engineers, the book includes computer code written in transportable Fortran so the reader can produce the numerical solutions and then extend them to other cases.

Customer Reviews:

The best book I've ever read.......2001-10-31

Just in general, i think this book is just soooo coool. I especially enjoyed the fourth order classical runge-kutta method. Professor Schiesser and Cesar knows what they are talking about, NO?

The essential work in this field........1999-01-09

Computational Transport Phenomena has been the single best general work I have found in my research into numerical heat and mass transfer problems. Clearly written, with excellent examples. Also includes well composed FORTRAN code samples.

Atomic and Molecular Beam Methods: Volume 2 (Atomic & Molecular Beam Methods)

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Atomic and Molecular Beam Methods: Volume 2 (Atomic & Molecular Beam Methods)

Manufacturer: Oxford University Press, USA
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Binding: Hardcover

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Book Description

This is the second volume of an advanced handbook on experimental molecular beam methods. As a continuation of the first volume, which covered general beam techniques and molecular beam scattering, the second volume covers beam spectroscopy and surface scattering. Both volumes, together or separately, can be used both as a reference book in the laboratory and as a supplementary text in graduate courses in chemical dynamics, spectroscopy and gas-surface interactions. In the present volume, the section on spectroscopy deals mainly with beam-laser interactions, but Fourier transform methods are covered as well. While the section on surface scattering deals primarily with crystalline surfaces, a separate chapter presents material on disordered surfaces. The emphasis of the book is on experimental methods, including data analysis and calibrations. However, the theory underlying the most common measurements is also presented to allow for the understanding of the numerous examples provided. Topics such as sub-doppler spectroscopy, photodissociation, molecular beam-masers, inelastic and reactive gas-surface collisions and others are discussed in detail. The text continues the study begun in Volume One, which focused on general beam technology and gas-gas scattering.

Modern Methods of Particle Size Analysis (Chemical Analysis: A Series of Monographs on Analytical Chemistry and Its Applications)

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Modern Methods of Particle Size Analysis (Chemical Analysis: A Series of Monographs on Analytical Chemistry and Its Applications)

Manufacturer: Wiley-Interscience
ProductGroup: Book
Binding: Hardcover

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ASIN: 0471875716

Book Description

Specialists in the field discuss the latest developments in particle size analysis, presenting an overview of state-of-the-art methodologies and data interpretation. Topics include commercial instrumentation, photon correlation spectroscopy, Fraunhofer Diffraction, field-flow fractionation, and detection systems for particle chromatography.

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