Classical Mechanics null edition Edition

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 Motion
Chapter 3. Momentum and Angular Momentum
Chapter 4. Energy
Chapter 5. Oscillations
Chapter 6. Calculus of Variations
Chapter 7. Lagrange's Equations
Chapter 12. Nonlinear Mechanics and Chaos
Chapter 13. Hamiltonian Mechanics

When 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.

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.

Fantastic book, especially for self-study. The author makes almost no assumptions about prior understanding, and tells you outright what he expects you to know. The examples are relevant and often difficult, and there are answers for plenty end of chapter problems in the back. The author makes a strong case for the importance of classical mechanics in a world dominated by headlines about more modern theories, and takes you on a journey you will not soon forget. For those who have a very solid grounding in Newtonian mechanics the first five chapters can be skipped.