Customer Reviews

A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (Cambridge Mathematical Library)

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To put it mildly, this book is a frightening exercise to read. The biggest challenge faced by modern readers is that we seem to have lost certain mathematical skills and intuition compared with people in the very early 1900's. It takes enormous amounts of patience and effort to try and work through any of the proofs or derivations presented in this book.

However, Whittaker has presented just about every concept in classical dynamics that you could possibly want to know in an extremely elegant fashion. Concepts that you simply do not expect to see in a book written first in 1904 make an appearence here. This book is worth reading just to find out how the original mathematicicals that invented concepts view them. For exmaple, Whittakers use of Christoffel Symbols is the classical view that the early geometers like Levi-Civita probably had, without the modern terminology and viewpoint in temrs of connections on a manifold.

All in all this book is well worth the time and effort spent to read it, but be prepared to use up lots of paper in your attempts to convince yourself that a single proof is true.(Brush up your geometry before you even try to read this book)

This book is, or rather was , the first modern book on classical mechanics. I think the first edition was published in 1904 and at the time it represented just about all that was known about the subject. A serious student today could rightly ask why he/she should read such a old book ? Well the answer to that question is a not an esay one : however whilst I would never say it is an simple book it repays careful study. Anyone taking more modern courses based on Arnold or Abraham and Marsden would do well to have a copy of this book by their side.The problems are taken mainly from Cambridge Maths Tripos examinations and they form a useful adjunct to the main body of the text.All the major topics are coverd including the 2 and 3 body problem, small oscillations, stability,etc. Well worth a read.

This is where I learned Liouville's integrability theorem for Hamiltonian systems, a key topic ignored by most modern texts on classical mechanics. Arnol'd covers it, but I found Arnol'd's more abstract lattice-based proof difficult to follow. Whittaker's text also contains many problems that are useful for a modern dynamics course. As a basis for understanding modern nonlinear dynamics, or for applications of mechanics, this old text is in many respects far better than the newer 'standard' mechanics texts by Landau-Lifshitz, and by Goldstein.

But take care: in a general discussion of integrability (conserved quantities) for general systems of odes early in the book, Whittaker does not distinguish local from global integrability. But then neither does Eisenhart in his book Continuous Groups, of the same era.

As the other reviewers put it, a classic. Well worth the price! My only comment is this facsimile edition is a scan of the original (not reset). Some of the formulae are small and not as clear as I wish-there is extensive use of the Newtonian notation for derivatives. It is usually ok to read, and context helps with meaning as does a reading glass.

This is the most referenced mechanics book in contemporary physics. In fact, it seems rather challenging to find a mechanics book written in the last hundred years that doesn't reference this work. As such, reading it is almost mandatory for the serious physics student. But before you read it, make absolutely sure that you are getting the fourth, and final, edition.

This is an odd book for the modern reader. It does not make any use of vector notation and assumes you have never seen a matrix before, even providing a rather quaint introduction to this "mysterious" topic toward the end. On the other hand, it absolutely expects you to have a solid working knowledge of elliptic functions. Reading both The elementary properties of the elliptic functions, with examples and Elliptic integrals beforehand and in that order should be enough for you to get by. In addition, some background in Spherical Trigonometry such as Spherical Trigonometry will prove helpful as well.

Also this book contains exactly four figures, and will never illuminate with a picture when half a page of careful text will do the job instead.

This is definitely a graduate level book even now, but one of the things that surprised me was the distinct lack of detail in some parts. Don't get me wrong: this will likely be the most detailed mechanics book you've ever read, but it may well leave you wanting more in some areas.

The first chapter is on Kinematics. It sets the stage well for the rest of the book. It offers some dated coverage of both quarternions and Cayley-Klein parameters for representing rotations. Euler angles are chosen as the canonical standard, although the convention employed differs from what I see most commonly adopted. However, the convention given here did win me over as I worked with it. The overall flavor of the chapter, and indeed the books as a whole, is very geometrical. And by geometry, I mean Euclid, not differential.

The second chapter is on equations of motion, and heads straight for Lagrange's formulation via D'Alembert's Principle. In the process it provides an excellent explanation of virtual displacements. It has a section on motion with reversed forces that uses the imaginary time formalism which I found very interesting.

Chapter three focuses on strategies and techniques for integrating the equations of motion. That is, finding integrals for them.

Chapter four treats soluble problems in particle dynamics. Among other problems, this chapter contains a detailed treatment of the circular and spherical pendulums making full use of elliptic functions. It uses the imaginary time formalism from chapter 2 to give a physical basis for the double periodicity of the elliptic functions which is quite satisfying.

Chapter five covers the dynamics of rigid bodies while chapter six treats the soluble problems of rigid body dynamics. The free rigid body is treated as well as the symmetric top. However, the detailed theory of herpolhodes developed in the nineteenth century is skipped and Kovalevsky's top receives cursory treatment. Apparently hyperelliptic functions are where this book draws the line.

Chapter seven treats vibrations while chapter eight takes up non-holonomic systems and dissipative systems.

Chapter nine discusses the principles of least action and of least curvature.

Chapter ten switches gears to Hamiltionian mechanics and covers Hamiltonian systems and their integral invariants, both absolute and relative.

Chapter eleven digs into canonical transformation theory while chapter twelve discusses the properties of integrals of dynamical systems.

Chapter thirteen begins working on the three body problem while chapter fourteen proves in detail the theorems of Bruns and Poincare regarding the absence of additional algebraic integrals other than the fairly obvious ones given in chapter thirteen. This is quite a daunting chapter, and the reader will need to be conversant with the elementary theory of algebraic functions to follow it.

Chapter fifteen is on the general theory of orbits and has a very nice section on orbits in general relativity. This chapter also contains all four of the previously mentioned figure in the book. However, I found its treatment of Riemannian geometry very interesting but entirely too superficial. This was one of the areas I felt the book really could have provided more meat.

The sixteenth and final chapter covers integration by series. It provides only the barest introduction to dynamical astronomy, but is quite challenging nonetheless.

Each chapter ends with a problem set, and many of the problems are quite difficult. Nonetheless, the book does provide quite a few worked examples throughout, and up through chapter six develops through these examples a rather methodical approach for analyzing particle and rigid body mechanics in a variety of situations which is alone worth the trouble of reading this book.

And while I initially thought the absence of vector notation was an annoyance, I actually considered it a virtue by the end much to my own surprise. There is definitely something to be said for brutal explicitness.

With all of that said, this should absolutely not be your first book on analytical mechanics. At a minimum, I would suggest already having The Variational Principles of Mechanics (Dover Books on Physics) under you belt. Lagrangian and Hamiltonian Mechanics is also worth working through first.

A difficult but rewarding work, although in all honesty in serious need of updating.