5 ms·

Structure and Interpretation of Classical Mechanics

101 points by xel02 16y ago

neutronicus 16y ago
I really like the idea of introducing classical mechanics and methods of numerical solution alongside one another. I do feel that physics at the undergraduate level fetishizes pencil and paper to the detriment of understanding how complex a classical system really can be. I am also ecstatic about the choice of not-Fortran for representing the algorithms. Makes me tempted to try and write a "Structure and Interpretation of Neutron Transport"
- jessriedel 16y ago
  I've taken several courses in classical mechanics, and I've never seen anyone give a proper treatment of complex (really, chaotic) systems unless the entire course in devoted to it. The ideas are so different and time-consuming that it just cannot be introduced alongside simple classical mechanics. That said, numerical simulations of simple systems (harmonic oscillators, perturbed oscillators, etc.) can be a helpful partner to analytical study.
- ericlavigne 16y ago
  Makes me tempted to try and write a "Structure and Interpretation of Neutron Transport" Let me know if you do - I'd be interested in reviewing early drafts. I studied nuclear engineering in grad school, but enjoyed the computational aspects enough to leave the field and start a career in programming instead. I don't recall liking any of the textbooks.
redsymbol 16y ago
I LOVE this book. I've had a hard copy for years. I always felt kind of lonely, though - it's such a niche topic that I had trouble finding anyone else interested enough to actually work through it :) So it's great to see it on the front page of HN. Its software, scmutils, includes an emacs-like editor and execution environment called Edwin. Here's an oooold blog post I wrote about using GNU Emacs with scmutils instead: http://ai.redsymbol.net/2007/06/using-gnu-emacs-with-scmutils.html http://ai.redsymbol.net/2007/06/using-gnu-emacs-with-scmutil...
- neutronicus 16y ago
  Depending on how much code is in this book I may be interested in porting it to work with Racket. I am very interested in investigating Lisps and Lisplikes for numerical work, so I'd be happy to work through it in parallel with you, if you're still looking for a partner.
- dice 16y ago
  It looks pretty interesting. I studied physics in school and have been thinking about going back for an MS in computational modeling, so I'm thinking I'll start in on this book over the weekend just for fun. I've never used a Lisp-like language before, and it looks to be a pretty comprehensive review of classical mechanics as well.
MrBlueSky 16y ago
Could the material in this book be reasonably accessible to somebody who has no calculus experience?
- neutronicus 16y ago
  No, not at all. The first equation is an integral.
  - mechanical_fish 16y ago
    Classical mechanics bears approximately the same relationship to calculus that calculus does to first-year algebra. You have to have a very good grasp of calculus to appreciate, or even survive, classical mechanics.
    - lutorm 16y ago
      Wasn't the reason Newton invented calculus so that he could calculate mechanics (i.e. Newton's Laws)?
      - zeynel1 16y ago
        if you mean calculus as taught today --no-- newton did not invent that calculus -furthermore- in newtons book known as -principia- newton does not use -calculus- in any shape or form to -calculate- orbits - newton uses only proportions -- but feel free to downvote me for daring to -question- such a cherished -myth- instead of reading -principia- for yourself
- grinich 16y ago
  The pre-reqs for the accompanying class include both single and multi-variable Calculus, as well as differential equations. http://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2005/ http://ocw.mit.edu/courses/mathematics/18-01-single-variable... http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/ http://ocw.mit.edu/courses/mathematics/18-02-multivariable-c... http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2006/ http://ocw.mit.edu/courses/mathematics/18-03-differential-eq... It's a long road, but a very rewarding one. Good luck.
namin 16y ago
I once took the MIT class on which this book is based: http://groups.csail.mit.edu/mac/users/gjs/6946/index.html http://groups.csail.mit.edu/mac/users/gjs/6946/index.html If anyone's interested, my problem sets solutions are here: http://www.cag.csail.mit.edu/~namin/mechanics/ http://www.cag.csail.mit.edu/~namin/mechanics/ The class was definitely out of my comfort zone in terms of the physics, but I loved the scheme system that allowed us to focus on the concepts, and leave the grunge to the computer. It's liberating to have an unambiguous notation, but it doesn't replace intuition.
jules 16y ago
> The dimension of the configuration space of the juggling pin is six: the minimum number of parameters that specify the position in space is three, and the minimum number of parameters that specify an orientation is also three. Can somebody explain this? Isn't the number of parameters that specify an orientation two, totaling five? Pick two atoms in the pin and specify the location of one atom. Now the other atom can only be located on a sphere around the first atom. The sphere is a 2d surface for which you need two parameters. Another problem is that you can encode two real numbers into one, for example by interleaving digits. So you could specify the entire pin with one real number. What exactly is the problem here and how can you eliminate it? You need to impose more conditions than simply continuity, because you can make a continuous bijection [0,1] <-> [0,1]^2? I really like the approach of this book. I often don't feel like I understand (or even know what there is to understand) something until I code a program for it. For example you understand collisions if you can write a program that given an initial configuration of polygons at t=0, gives the configuration at later time. If you don't do this then you don't know exactly what you understand. Perhaps you understand collisions of point masses, but not general collisions.
- ericlavigne 16y ago
  The dimension of the configuration space of the juggling pin is six: the minimum number of parameters that specify the position in space is three, and the minimum number of parameters that specify an orientation is also three. The quote comes from section 1.2 on configuration spaces. http://mitpress.mit.edu/sicm/book-Z-H-9.html http://mitpress.mit.edu/sicm/book-Z-H-9.html Can somebody explain this? Isn't the number of parameters that specify an orientation two, totaling five? Pick two atoms in the pin and specify the location of one atom. Now the other atom can only be located on a sphere around the first atom. The sphere is a 2d surface for which you need two parameters. It is not enough to specify the position of two atoms. You need to specify the positions of three atoms. The first atom can go anywhere, so it contributes 3 parameters. The second atom is limited to the 2-D surface of a sphere around the first atom, so its position only contributes 2 parameters as you said. The third atom is limited to the 1-D edge of a circle around an axis that connects the first two atoms, so its position contributes 1 parameter. If you choose the position of the point of a pencil, and also a point in the center of the pencil's eraser, the pencil can still spin, with the pencil lead as the axis. Another problem is that you can encode two real numbers into one, for example by interleaving digits. So you could specify the entire pin with one real number. What exactly is the problem here and how can you eliminate it? You need to impose more conditions than simply continuity, because you can make a continuous bijection [0,1] <-> [0,1]^2? The concept of dimension of a vector space is handled much more rigorously in proof-oriented linear algebra textbooks. This book gives a loose definition for the dimension of a configuration space, which is just good enough to be able to follow the issues they are talking about. You looked too closely at their definition and discovered a flaw. Dimension is not really the number of parameters required for encoding a position in the space, but this can still be a good enough working definition for many problems if you don't get too fancy about your encoding.
_corbett 16y ago
I also once took the course on which this book is based at MIT. A programmer by trade at the time, I found out a bit more about my learning style. Namely, I was able to relatively easily complete the assignments without developing a very deep understanding of classical mechanics along the way. It was only later in physics graduate school, and after semesters of doing calculations by hand, that I was able to put my previous work in a larger context. I'd love to revisit the course with that new perspective and a bit more time than that haggered MIT student of yore. In summary I'd echo another poster's comment that "it's liberating to have unambiguous notation but it doesn't replace intuition".
realitygrill 16y ago
I'd like to point out that, in addition to SICM and SICP, there is also a SIQM - Structure and Interpretation of Quantum Mechanics. Always hoped there were going to be more of these books.

101 points by xel02 16y ago

I really like the idea of introducing classical mechanics and methods of numerical solution alongside one another. I do feel that physics at the undergraduate level fetishizes pencil and paper to the detriment of understanding how complex a classical system really can be. I am also ecstatic about the choice of not-Fortran for representing the algorithms. Makes me tempted to try and write a "Structure and Interpretation of Neutron Transport"

jessriedel 16y ago
I've taken several courses in classical mechanics, and I've never seen anyone give a proper treatment of complex (really, chaotic) systems unless the entire course in devoted to it. The ideas are so different and time-consuming that it just cannot be introduced alongside simple classical mechanics. That said, numerical simulations of simple systems (harmonic oscillators, perturbed oscillators, etc.) can be a helpful partner to analytical study.
ericlavigne 16y ago
Makes me tempted to try and write a "Structure and Interpretation of Neutron Transport" Let me know if you do - I'd be interested in reviewing early drafts. I studied nuclear engineering in grad school, but enjoyed the computational aspects enough to leave the field and start a career in programming instead. I don't recall liking any of the textbooks.

redsymbol 16y ago

I LOVE this book. I've had a hard copy for years. I always felt kind of lonely, though - it's such a niche topic that I had trouble finding anyone else interested enough to actually work through it :) So it's great to see it on the front page of HN. Its software, scmutils, includes an emacs-like editor and execution environment called Edwin. Here's an oooold blog post I wrote about using GNU Emacs with scmutils instead: http://ai.redsymbol.net/2007/06/using-gnu-emacs-with-scmutils.html http://ai.redsymbol.net/2007/06/using-gnu-emacs-with-scmutil...

neutronicus 16y ago
Depending on how much code is in this book I may be interested in porting it to work with Racket. I am very interested in investigating Lisps and Lisplikes for numerical work, so I'd be happy to work through it in parallel with you, if you're still looking for a partner.
dice 16y ago
It looks pretty interesting. I studied physics in school and have been thinking about going back for an MS in computational modeling, so I'm thinking I'll start in on this book over the weekend just for fun. I've never used a Lisp-like language before, and it looks to be a pretty comprehensive review of classical mechanics as well.

MrBlueSky 16y ago

Could the material in this book be reasonably accessible to somebody who has no calculus experience?

neutronicus 16y ago
No, not at all. The first equation is an integral.
- mechanical_fish 16y ago
  Classical mechanics bears approximately the same relationship to calculus that calculus does to first-year algebra. You have to have a very good grasp of calculus to appreciate, or even survive, classical mechanics.
  - lutorm 16y ago
    Wasn't the reason Newton invented calculus so that he could calculate mechanics (i.e. Newton's Laws)?
    - zeynel1 16y ago
      if you mean calculus as taught today --no-- newton did not invent that calculus -furthermore- in newtons book known as -principia- newton does not use -calculus- in any shape or form to -calculate- orbits - newton uses only proportions -- but feel free to downvote me for daring to -question- such a cherished -myth- instead of reading -principia- for yourself
grinich 16y ago
The pre-reqs for the accompanying class include both single and multi-variable Calculus, as well as differential equations. http://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2005/ http://ocw.mit.edu/courses/mathematics/18-01-single-variable... http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/ http://ocw.mit.edu/courses/mathematics/18-02-multivariable-c... http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2006/ http://ocw.mit.edu/courses/mathematics/18-03-differential-eq... It's a long road, but a very rewarding one. Good luck.

namin 16y ago

I once took the MIT class on which this book is based: http://groups.csail.mit.edu/mac/users/gjs/6946/index.html http://groups.csail.mit.edu/mac/users/gjs/6946/index.html If anyone's interested, my problem sets solutions are here: http://www.cag.csail.mit.edu/~namin/mechanics/ http://www.cag.csail.mit.edu/~namin/mechanics/ The class was definitely out of my comfort zone in terms of the physics, but I loved the scheme system that allowed us to focus on the concepts, and leave the grunge to the computer. It's liberating to have an unambiguous notation, but it doesn't replace intuition.

jules 16y ago

> The dimension of the configuration space of the juggling pin is six: the minimum number of parameters that specify the position in space is three, and the minimum number of parameters that specify an orientation is also three. Can somebody explain this? Isn't the number of parameters that specify an orientation two, totaling five? Pick two atoms in the pin and specify the location of one atom. Now the other atom can only be located on a sphere around the first atom. The sphere is a 2d surface for which you need two parameters. Another problem is that you can encode two real numbers into one, for example by interleaving digits. So you could specify the entire pin with one real number. What exactly is the problem here and how can you eliminate it? You need to impose more conditions than simply continuity, because you can make a continuous bijection [0,1] <-> [0,1]^2? I really like the approach of this book. I often don't feel like I understand (or even know what there is to understand) something until I code a program for it. For example you understand collisions if you can write a program that given an initial configuration of polygons at t=0, gives the configuration at later time. If you don't do this then you don't know exactly what you understand. Perhaps you understand collisions of point masses, but not general collisions.

ericlavigne 16y ago
The dimension of the configuration space of the juggling pin is six: the minimum number of parameters that specify the position in space is three, and the minimum number of parameters that specify an orientation is also three. The quote comes from section 1.2 on configuration spaces. http://mitpress.mit.edu/sicm/book-Z-H-9.html http://mitpress.mit.edu/sicm/book-Z-H-9.html Can somebody explain this? Isn't the number of parameters that specify an orientation two, totaling five? Pick two atoms in the pin and specify the location of one atom. Now the other atom can only be located on a sphere around the first atom. The sphere is a 2d surface for which you need two parameters. It is not enough to specify the position of two atoms. You need to specify the positions of three atoms. The first atom can go anywhere, so it contributes 3 parameters. The second atom is limited to the 2-D surface of a sphere around the first atom, so its position only contributes 2 parameters as you said. The third atom is limited to the 1-D edge of a circle around an axis that connects the first two atoms, so its position contributes 1 parameter. If you choose the position of the point of a pencil, and also a point in the center of the pencil's eraser, the pencil can still spin, with the pencil lead as the axis. Another problem is that you can encode two real numbers into one, for example by interleaving digits. So you could specify the entire pin with one real number. What exactly is the problem here and how can you eliminate it? You need to impose more conditions than simply continuity, because you can make a continuous bijection [0,1] <-> [0,1]^2? The concept of dimension of a vector space is handled much more rigorously in proof-oriented linear algebra textbooks. This book gives a loose definition for the dimension of a configuration space, which is just good enough to be able to follow the issues they are talking about. You looked too closely at their definition and discovered a flaw. Dimension is not really the number of parameters required for encoding a position in the space, but this can still be a good enough working definition for many problems if you don't get too fancy about your encoding.

_corbett 16y ago

I also once took the course on which this book is based at MIT. A programmer by trade at the time, I found out a bit more about my learning style. Namely, I was able to relatively easily complete the assignments without developing a very deep understanding of classical mechanics along the way. It was only later in physics graduate school, and after semesters of doing calculations by hand, that I was able to put my previous work in a larger context. I'd love to revisit the course with that new perspective and a bit more time than that haggered MIT student of yore. In summary I'd echo another poster's comment that "it's liberating to have unambiguous notation but it doesn't replace intuition".

realitygrill 16y ago

I'd like to point out that, in addition to SICM and SICP, there is also a SIQM - Structure and Interpretation of Quantum Mechanics. Always hoped there were going to be more of these books.