Structure and Interpretation of Classical Mechanics | Hacker News Reader

Structure and Interpretation of Classical Mechanics

mitpress.mit.edu

153 pointsluu37 comments

Just to note for people who know about SICP: this book is not like that. The book jumps straight into basic principles of Lagrangian mechanics, talking about the least action principle and the Euler-Lagrange equations. It is not "mechanics 101 for smart people" like SICP is for computer science.

With that said, the computational approach they take is unique and useful. You'd especially like it if you like Scheme and the coding style found in SICP.

Learning Lagrangian mechanics was like falling in love all over again with your girlfriend when you discovered exactly how elegant she could be. Easily my favorite part of classical mechanics as an undergrad.

Same here. In highschool, I really struggled with classical mechanics. A lot of things didn't click, because they were taught to us before we were taught calculus, and a lot of what I was seeing in class simply didn't make much sense. I understood the words and I could do the math, but never actually felt like I had a grip on it.

Fast forward to my freshman year and poof! mechanics suddely isn't a mess of because-i-said-so formulae that sort of make some physical sense. It's an elegant, well-thought system that can help you understand the world.

I had a further moment of revelation later on, when I seriously studied philosophy. It doesn't look like much now, but when put into their historical context, the discoveries made by Galilei and Newton are amazing leaps in human thought.

Microeconomics is as bad as physics in that respect -- if the course doesn't assume calculus, they wind up reinventing anyway. It's not worth the trouble to study either subject unless knowledge of calculus is assumed.

This. Exactly this, and I think it's not a coincidence that learning Scheme was also like this, but for programming.

On the idea of "mechanics 101 for smart people" - can anyone recommend good books that are the analogs of SICP for other subjects? I'd love to know ones for, say, genetics or evolution as well as stats.

I can say that Hubbard + Hubbard "Vector Calculus, Linear Algebra, and Differential Equations" does a good job of being that for vector calculus specifically and for exposure to theoretical mathematics.

I'm currently preparing for a course based around The Theoretical Minimum by Leonard Susskind, which (so far) seems like exactly what you're looking for. The beginning has a very quick recap of state spaces, vectors, calculus, etc. It goes over Lagrangian mechanics and conservation laws in the middle before finishing with Poisson brackets.

The table of contents also claims a chapter on E&M, but I haven't looked at that yet.

Almost finished Vol I of Feynman Lectures On Physics. So far, Im picking up on the same enthusiasm and joy. A real pleasure to read.

Euclid's Elements too for geometry is fantastic. (I think reading "from the horses mouth" is necessary but not sufficient. With guys like Newton especially, since there are no translation barriers (for us English speakers), and they are quite relatable.)

I have noticed that excursions? in history of a topic; its people, places, culture, enhance the quality of the book. Feynman goes on historical asides, as does say, Apostol (in his calculus texts), and it has been a while but I believe SICP does too. I think the teaching of something should be coupled with its history.

In this same vein, I'm too am interested in a book covering evolution and biology, but I have not found one, or heard of one, so if anybody knows I would greatly appreciate it. Two good bio books I have read are The Selfish Gene, and The Machinery Of Life (Goodsell), but they're more auxiliary.

I'm quite fond of Watson's Molecular Biology of the Gene (not to be confused with Molecular Biology of the Cell).

In the stats camp, Jaynes is fantastic, alas a bit difficult. But the prerequisites are very modest. It's self-contained.

Hoel, Port & Stone's volume is a great introduction to basic (w/o measure theory) probability.

On a more elementary level, Michael Spivak's Calculus is an amazing book on first-year calculus.

He also wrote Calculus on Manifolds and a 5-volume series on Differential Geometry. Those, to put it mildly, were rougher going.

I actually once got a crush on a dorm-mate in large part because I saw Calculus on Manifolds on her bookshelf. It wasn't reciprocal, however. Later in life, she went on to run the Bureau of Labor Statistics.

> I actually once got a crush on a dorm-mate in large part because I saw Calculus on Manifolds on her bookshelf. It wasn't reciprocal, however. Later in life, she went on to run the Bureau of Labor Statistics.

I had someone I'd never met before see my copy which happened to be the international edition (in Chinese, with English in the back) and then assume I spoke fluent Mandarin. Your story's a lot better :)

I lived 3 years in a Harvard grad school dormitory. One meets a variety of interesting people in such a place. E.g., I once pitched a foreign policy maven dorm-mate on caring more about Africa ... and it was http://en.wikipedia.org/wiki/Paula_Dobriansky, who 25 years later had a very major role in combating AIDS. But http://en.wikipedia.org/wiki/Daniel_Pipes was a jerk who couldn't stomach losing to a math student at Scrabble. :)

Yeah Hubbard & Hubbard that I recommended is a more approachable take on Calculus on Manifolds (which it is based on or inspired by). It's still not simple, but it's probably a bit easier-going for the modern student than Spivak.

I remember being disappointed with Calculus on Manifolds, since it was very abstract. I was looking for something with more explicit calculations. To this end, I was quite happy with Edwards "Advanced Calculus"

http://www.amazon.com/Advanced-Calculus-David-V-Widder/dp/04... http://www.amazon.com/Advanced-Calculus-Several-Variables-Ma...

I'm a big fan Landau and Lifshitz's "Mechanics." Starting from nothing they hit the major results in classical mechanics in 224 pages. Short. Sweet. Elegant.

For statistics I can really recommend 'All of Statistics' by Larry Wasserman (http://www.stat.cmu.edu/~larry/all-of-statistics/)

It runs through a lot of important topics, particularly in inference, without being either as turgid as most stats texts for people without a maths background or as dry as more 'pure' books (no measure theory required).

For biology I'd recommend 'Physical Biology of the Cell' (http://microsite.garlandscience.com/pboc2/) if you like to think quantitatively. About evolution specifically I find Schrodinger's 'What is Life?' thought-provoking if you already know the basics.

"A course in mathematics for students of physics" (volumes 1 and 2) by Paul Bamberg and Schlomo Sternberg. [1] [2]

I loved both the books! I replaced my course textbooks with these and am eternally thankful I did that. Volume 2, in particular, is really cool where you get introduced to the exterior calculus formulation of circuit theory, leading to Maxwell's equations.

[1] http://www.amazon.com/Course-Mathematics-Students-Physics/dp... [2] http://www.amazon.com/Course-Mathematics-Students-Physics-Vo...

Doesn't Feynman Lectures do that? http://feynmanlectures.caltech.edu/I_toc.html

Neat.

Does anyone have a epub/mobi version of this book?

What would be good prerequisite reading before SICM?

At least an understanding of:

* Newtonian mechanics

* Multivariable calculus

* Ordinary differential equations

* Basic functional programming, Scheme, SICP

* A developed discipline for reading higher level mathematical material, including new notations and ideas

For those interested, Leonard susskin video course in stanford ( can be found anywhere ) on classical mechanics is one of the most beautiful piece of intellectual material i've ever been given the chance to see.

How do Susskind’s lectures compare to Walter Lewin’s lectures?

They're completely different.

Susskind won't teach you things like friction, drag, or elasticity. But, he will teach you some of the most profound theoretical insights of modern physics.

Lewin won't teach you Euler-Lagrange Equations, or Noether's Theorem. But, he will teach you how to think about solving practical physics problems.

They also have different sense of humour:

http://www.youtube.com/watch?v=ApUFtLCrU90#t=49m27s

And how do both compare to Penrose's Road To Reality and the Feynman Lectures on Physics?

FLOP and Susskind's Theoretical Minimum are similar in that they both aim to teach an intuition of theoretical physics, rather than training one to do calculate the solutions of particular physics problems. So, they are similar in that respect.

The key difference that I noticed is that Feynman's intention is to explain nature, and he tends to avoid relying too heavily on the mathematics as part of that explanation.

Susskind's focus is on raw abstractions themselves, often independent of the physical phenomena that are being abstracted. His intent is to exaplain the mathematics, and to give you an intuition and appreciation for the beauty of those abstractions.

For example, Feynman shows you the Lorenz Transformations and says "this is the stuff that is needed to make Maxwell's Equations work out the same to a moving observer." On the other hand, Susskind starts with the notion that light has the same velocity in all reference frames, and uses this to derive the Lorenz Transformations algebraically.

I haven't read Penrose, so I can't comment on that.

Reaching noether's theorem really was the climax of this course. Such a great memory.

I absolutely agree. I hit the first chapter of SICM like a brick wall on my first attempt, but after watching Susskind's lectures I found it far easier to understand (although it is still a very difficult book!)

http://theoreticalminimum.com/courses/classical-mechanics/20...

Yes, it was amazing. The good news is that it was turned into a book, The Theoretical Minimum. The bad news is that the book was really disappointing. I'm more of a learn-by-reading than learn-by-watching person, but Susskind's lectures are amazing.

I don't think a book could ever compare to 20 hours of classroom video when you've got the chance to have such a great professor. The pace, repititions, emphasis, hands gesture, hesitations, pauses, are also helping you understand and digest the course ( as with every human communication). Frankly what Mr susskind has done with this stanford program is truely the work of a great man.

I just watched the first 2 videos, they are great. Thank you!

If you've got an ipad, i recommend using itunes univeristy to download all the courses. I've spent a whole summer watching those under a tree. Most memorable online course experience you can dream of.

PDF typeset with LaTeX edition: http://www.fisica.net/mecanicaclassica/struture_and_interpre...

For those who have not seen it, this is based on SCMUTILS -- an open source symbolic manipulation engine, much like Mathematica or Maple. It is extremely powerful, and the book is worth reading just to understand the design patterns used there.

To give an example, in a dozen lines of readable, intuitive code, you can:

* write a lagrangian as a normal Scheme function

* symbolically take derivatives of that to get equations of motion

* print those equations with LaTeX.

* compile those equations to native code and numerically integrate and plot the motion of the system

It's like magic the first time you see it.

ever since watching sussman's talk http://www.infoq.com/presentations/We-Really-Dont-Know-How-T... i've been curious to see these details. really good post.

the jibe about, "our competitors," at the end of the preface left a bad taste in my mouth, though. i'd really like to think that was tongue-in-cheek and people as tenured as these guys, if anyone, can afford to think of math and science as the collaborative effort that it is rather than a competition.

Wow! Last night I picked up Dirac's little "Lectures on Quantum Mechanics" and stumbled at the start because my '60s mechanics education didn't include the Lagrangian, much less the Hamiltonian.

Today comes this and it should be more than enough for me to give Dirac another solid whack! Maybe enough, even, to come out the other side given another fundamental or two.

Comparing this page to the Feynman Lectures from earlier in the week, it's really amazing how far latex typography has come in the last few years. Now we all use MathJax.

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