Classical Mechanics [CLASSICAL MECHANICS] [Hardcover] Hardcover – September 1, 2004

When I was a college student, my classroom textbook on classical mechanics was Classical Mechanics by Simons. I remember that the classical mechanics class was never inspiring although I had a dream that I want to be a great physicist, and so I was very interested in physics. The professor of the class concentrated on conveying the contents of the textbook, in particular, the skills to solve problems to students, although I wanted to understand the principles more deeply. Now, I am looking over Simons' book, and I find that it contains all the needed materials on classical mechanics, but it is somewhat "dry" and difficult to read.Studying physics again, after I got doctoral degree in mathematics, I have had to study Lagrange's equations and Hamiltonian mechanics. Instead of re-reading Simons' book or trying Goldstein's book, I chose J. Taylor's Classical Mechanics for my self-study, because the Amazon.com reviews on Taylor's book were of full praises. Now, I truly appreciate the reviewers. They were right. This book is really great!As do many other people, I had no time to read the entire book. So I read only the chapters on Lagrange's equations, Hamiltonian mechanics, and Chaos as well as some earlier chapters. Here, I list the chapters that I read.Chapter 1. Newton's Laws of MotionChapter 3. Momentum and Angular MomentumChapter 4. EnergyChapter 5. OscillationsChapter 6. Calculus of VariationsChapter 7. Lagrange's EquationsChapter 12. Nonlinear Mechanics and ChaosChapter 13. Hamiltonian MechanicsWhen reading the earlier chapters, sometimes I wanted to quit because of some dissatisfaction. His explanations of the definition of mass and force were not to my taste. But I disregarded my discontent because other authors such as Susskind, Shankar, and Simons were also a little unsatisfactory in this regard. For another example, whilst he explains how to solve a second-order, linear, homogeneous differential equations, he omitted explanations about whether the constants he was using were real or complex. So if the readers cannot fill in the details themselves, these parts can be confusing. Moreover, at some places in the early chapters, his mathematical expressions are not so good. For example, he uses the expression dy = (dy/dx) dx and for a function f, he seems to regard the differential df as an infinitesimal quantity. All the formulae he uses are mathematically correct, but I think if the readers do not have a firm understanding of calculus, it can be misunderstood. I thought that all the mathematics in the later part of the book would be unsatisfactory, but, after finishing the book, I found that his understanding of mathematics is truly sound and accurate. As an example, I would like to quote the following."(P530) The derivative dH(q_1,..,q_n, p_1,..,p_n,t)/dt is the actual rate of change of H as the motion proceeds, with all the coordinates q_1, ...,q_n, p_1, ...,p_n changing as t advances. ∂H/∂t is the partial derivative, which is the rate of changing of H if we vary t holding all the other arguments fixed. In particular, if H does not depend explicitly on t, this partial derivative will be zero"I first encountered the Euler-Lagrange equation and Hamiltonian mechanics in the classical mechanics course mentioned above. Compared with that experience, Taylor's book is truly reader-friendly. As you may know, the three mechanics by Newton, Lagrange and Hamilton are equivalent. The author makes efforts to explain that, if so, why we study all three. I have read some books or papers containing elementary introductions to Lagrange's and Hamiltonian mechanics. But only after reading this book, I was able to understand that Lagrange's formulation is superior when we study constrained mechanical systems, whilst Hamiltonian mechanics is better than Lagrange's approach when we have to consider the phase space. Taylor's book was the best introduction to Lagrange's and Hamiltonian mechanics. As an example of how meticulous Taylor is in explaining his ideas, I quote the following."(P251) Actually, it is a bit hard to imagine how to constrain a particle to a single surface so that it can't jump off. If this worries you, you can imagine the particle sandwiched between two parallel surfaces with just enough gap between them to let it slide freely."My favorite chapter of the book was Chapter 12: Nonlinear Mechanics and Chaos. About chaos, I have read some books by Gleick, Stewart, and Strogatz, etc. But for me, Taylor's Chapter 12 was best. The greatest merit of the book is that the author concentrates on only two examples: the driven damped pendulum and the logistic map. By studying the behaviors of these two concrete examples under changing parameters, he explains the fundamental concepts of nonlinear dynamics such as the Feigenbaum number, bifurcation diagram, state-space, and Poincare sections. I have read a lot about the Feigenbaum number in other books, but I couldn't understand what it is exactly. Only after reading Taylor's book, I was able to understand what Feigenbaum number is. If you have read Gleick's book and thought it somewhat vague, I recommend you to read Chapter 5: Oscillations and Chapter 12: Nonlinear Mechanics and Chaos. One thing I hoped about the chapter on chaos was how great it would be if the chapter were to deal with renormalization. I appreciate the author for writing such a nice book about classical mechanics.

First thing’s first, Taylor covers a lot of material. A surprising amount of material. This is arguably one of the most self-contained mechanics books I’ve seen. He develops everything from newton’s laws to continuum mechanics in surprisingly good detail. The best thing about John Taylor’s book is something very underrated about a lot of textbooks, he MOTIVATES ideas.What I like:One place I ESPECIALLY want to highlight is his section on calculus of variations. I think his treatment of variational calculus and the Lagrangian and the Hamiltonian are among the best I’ve seen in any book. He clearly states that the lagrangian is a functional for a path integral in a velocity-position phase space, and that Euler Lagrange equations are a result of minimizing the path integral, which is really just a manifestation of the principle of least action. Chapter 6 and 7 of Taylor is arguably one of the best I’ve ever read. His treatment of variational calculus is both visual, sufficiently rigorous, and backed by motivation and he always compares and contrasts with newton’s laws. One might take issue with the fact that he only deals with time-independent systems, but that’s not necessarily a bad thing because that’s where the Lagrangian is best at. His treatment of Hamiltonians is not as good, but chapter 13 (where he develops the Hamiltonian formalism) is nonetheless excellent. He derives Hamiltonians in a semi-rigorous manner and gives great motivation on the differences and advantages and disadvantages of the various formulations of mechanics. And it’s also because Hamiltonians are not as useful as the Lagrangian in a classical setting because it’s easier to write everything in terms of velocities for macroscopic systems, whereas in quantum mechanics, everything is built off of the commutation relation of position and momentum, the uncertainty principle, and the infinitesimal generation of unitary operators by self-adjoint operators in accordance with Noether’s Theorem. If you’re looking to learn calculus of variations and Lagrangian and Hamiltonian formalisms of mechanics, come to this book.Few other sections that are noteworthy for being good are his treatments of rotating reference frames and his treatment of normal modes and chaotic dynamics. There is a surprisingly good amount of nonlinear dynamics treated in this book, even if it’s not usually in the scope of classical mechanics per say.What I don’t like:I love Taylor is extremely easy to read, partly because the most math it assumes is multivariable calculus and basic matrix algebra. But, I don’t like the mathematical maturity of this book. There are certain topics that are significantly easier and more intuitive with good linear algebra formalism (rigid body dynamics, relativity, etc). Taylor’s treatment of Euler angles and his explanation of the space frame and body frame are not my favorite personally, and introducing rotation matrices and change of basis would have made these significantly easier to view rather than trying to gain physical intuition behind an already confusing topic. And his treatment of special relativity is extremely thorough, but his formalism is outdated and he only offers input about the consequences of relativistic effects and nothing about the underlying geometry of the flat Minkowski space and the Lorentzian metric. Definitely recommend getting another book just for relativity because it’s a dense subject requiring lots of advanced mathematical formalism (way past linear algebra unfortunately). His first 5 chapters are nothing to write home about, although I do enjoy his comments on the harmonic oscillator and each case of damping (in chapter 5). He even has a nice little section on Fourier series and solving differential equations.Weird:Chapter 14 is among the weirdest I have ever seen. He talks about the hard sphere collision and proceeds to derive Rutherford scattering. Oddly enough, he delves rather deep into calculating cross sections and explaining what a cross section of a scattering reaction is, which is extremely out of place, but interesting nonetheless.Enough said. I highly recommend. This is a classic.

I’ve been retired for about a year as a high school physics teacher and took on this book as a “recreational project”. This book is a winner! I highly recommend it for anyone wanting to self-study the topic of classical mechanics. I found it to be extremely well written and excellent in every way! Having grown up with Symon’s “Mechanics” back in the 1960’s I was wondering how Taylor’s “Classical Mechanics” compared. Symon’s book was known for its almost impossible problems but I was excited to find Taylor’s book had an array of problems with basically 3 different levels of difficulty: One star (easy), two stars (medium), and 3 stars (hard). I was successful with most of the one and two star problems which gave me self-confidence to keep working my way thru the book.I went through chapters 1-11 (the first 454 pages) as recommended, then skipped to the “Further Topics” section. In the “Further Topics” I chose to do chapter 13 on Hamiltonian Mechanics and chapter 15 on Special Relativity.Taylor explains things in a wonderfully understandable way with many examples throughout. The mathematics is rigorous and beautifully developed as needed throughout. John Taylor is a “teacher”, not just a smart professor who knows a lot but doesn’t know how to communicate it.A basic understanding of calculus and elementary differential equations is all that is needed. The only trouble I encountered was in chapter 15 on Special Relativity with the utilization of “4-Vectors”. Implementing that topic could have been done more thoroughly and more slowly for me anyway. Otherwise I have no complaints.Odd number answers are given. Many of the problems from Taylor’s book with answers and solutions can be found on the internet.