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Structure and Interpretation of Classical Mechanics

by dennybritz on 5/12/20, 1:33 PM with 40 comments

  • by formalsystem on 5/12/20, 3:15 PM

    This is a great book but a bit dense first. At a high level it goes through physics with an optimization viewpoint, as in find the actions that minimize a system's energy to figure out how a system will evolve.

    I would strongly suggest you learn Lagrangian and Hamiltonian Mechanics from this book first [1] since it comes with many more illustrations and simple arguments that'll make reading SICM much easier. If you don't have time to read a whole book and want to get the main idea I've written a blog post about Lagragian mechanics myself [2] which has made it to the front page of Hacker News before. The great thing about SICM is that it's a physics textbook where the formulas are replaced by code [3] which you means you can play around with your assumptions to gain intuition for how everything works.

    IMO I believe in introductory physics we overemphasize formalism over intuition and playing around with simulators is a truer way to explore physics since most physical laws were derived via experimentation not derivation. Another book that really drives this point home is [4]

    [1] https://www.amazon.com/Jakob-Schwichtenberg/dp/1096195380/re...

    [2] https://blog.usejournal.com/how-to-turn-physics-into-an-opti...

    [3] https://github.com/hnarayanan/sicm

    [4] https://natureofcode.com/

  • by tgvaughan on 5/12/20, 4:08 PM

    I love what I've read of this book, but found reading the HTML version on the MIT website a bit of a chore. Here's my attempt at applying Andres Raba's wonderful SICP layout (https://sarabander.github.io/sicp) to SICM: https://tgvaughan.github.io/sicm

  • by kragen on 5/12/20, 3:40 PM

    SICM has been on my list of things to study for years, but I haven't made it much past the delightful preface:

    > When we started we expected that using this approach to formulate mechanics would be easy. We quickly learned that many things we thought we understood we did not in fact understand. Our requirement that our mathematical notations be explicit and precise enough that they can be interpreted automatically, as by a computer, is very effective in uncovering puns and flaws in reasoning. The resulting struggle to make the mathematics precise, yet clear and computationally effective, lasted far longer than we anticipated. We learned a great deal about both mechanics and computation by this process. We hope others, especially our competitors, will adopt these methods, which enhance understanding while slowing research.

    This second edition is from 2015, following the 2001 first edition.

    Unfortunately, unlike SICP, it does not seem to be under a free license, so it is not legal to translate it into Spanish or produce a reformatted digital version that incorporates an actual Scheme interpreter.

  • by thatcherc on 5/12/20, 3:18 PM

    There's a ton to learn from this book, especially if both Scheme (or functional programming in general) and the Lagrangian and Hamiltonian formulations of mechanics are new to you as they were to me when I first came across the text online. I ended up taking the class in person and seriously enjoyed it. It was a big reason I switched my major from CS to physics, which I mean in the best way possible! I think the authors were right in their assessment that Lisps are really well suited to mathematics, and especially the type of math you see in working with Lagrangians: function composition and partial application. Plus there's the cool benefit of being able to write code that looks at other code and writes its derivative as a new program!

    The two small warnings I would share with someone starting this book are

    1) they introduce some of their own notation to clarify, i.e., what various derivatives mean, but this notation is different than what is found in other texts

    2) it ramps up pretty quickly from solving a double pendulum to much higher-level stuff like Lie transforms and perturbation theory - it's a lot to keep in your head all at once. Don't get discouraged if you hit a wall and need to come a couple days or weeks or months later - I definitely did, and it is still fun to try to go back and make it through the harder parts. Highly recommend!

  • by montalbano on 5/12/20, 5:49 PM

  • by Myrmornis on 5/12/20, 4:48 PM

    This book's amazing. I've only tried to understand the first few chapters so far but I found the basic idea -- reformulating the Euler-Lagrange equations in lisp, and using Spivak's alternative notation for differential calculus -- to be extremely illuminating and even inspiring when going back and trying to really make sense of (advanced) undergrad calculus.

    OK, so here's my question: the scheme is great and all, but wouldn't this really benefit from a statically typed language with a rich type system? I think it would be really interesting to try to make the computations at the type level correct as well as at the runtime level. Obvious candidates I guess are Haskell/OCaml etc, or one of the theorem-proving languages (out of my depth here, but Lean/Coq etc).

    I have said this before...another HN thread on SICM: https://news.ycombinator.com/item?id=21460106

  • by enriquto on 5/12/20, 3:34 PM

    If you are more mathematically inclined, there's also "Functional Differential Geometry" by the same authors, and in the same spirit, but much shorter. The goal of the book is essentially to write the Euler-Lagrange equations in lisp, which is a breathtakingly beautiful thing.

  • by dennybritz on 5/12/20, 3:30 PM

    I posted this because it was recommended to me several times in [0], together with several other "computational approaches to Physics" books, and thought it would be interesting to HN users. If you're looking for more books like this, the whole Twitter thread is worth a read. It's full of good recommendations.

    [0] https://twitter.com/dennybritz/status/1260137814982787073

  • by Cleonis on 5/13/20, 9:10 PM

    I have a hard copy of the first edition. The dedication says: "dedicated to the principle of least action"

    I have an educational resource for introduction to Hamilton's stationary action. The title is "Least action visualized".

    http://www.cleonis.nl/physics/phys256/least_action.php

    The diagrams on the page have a slider for active exploration. Moving the slider sweeps out a range of trial trajectories. As you change the trial trajectory the diagram shows how the graphs of the energies come out accordingly.

    In this resource Hamilton's stationary action is introduced in a two-stage process.

    First stage: We have the Work-Energy theorem, which we can apply with equal validity in infinitisimal form. The true trajectory has the following obvious property: at every instant in time the rate of change of potential energy matches the rate of change of kinetic energy. Demanding this match as a condition we identify the true trajectory among the range of trial trajectories. That is, this initial stage is already variational approach, but it doesn't yet use the concept of action.

    Second stage: Demonstration of moving in a single step from the first stage to Hamilton's stationary action.

    The demonstration is for the simplest case: a uniform force, hence a linear potential. The reasoning generalizes to all cases.

  • by djaque on 5/12/20, 3:36 PM

    I did a read through last year and thought it was great. Having to actually tell a computer how to do Langrangian and Hamiltonian mechanics makes you learn it really well. Pointed out some of the interesting reasons behind why we choose or Langarangians/Hamiltonians the way we do that I didn't appreciate during undergrad.

  • by billfruit on 5/12/20, 5:40 PM

    One of the good things I felt about the book, though I have read only a few chapters is that, the use the Scheme-based system, has made the notation more concrete and lucid. No vague and confusing notations like the traditional treatment.

  • by enitihas on 5/12/20, 3:29 PM

    Amazingly, this book has the same author as SICP, i.e , Structure and Interpretation of Computer Programs.