
Structure and Interpretation of Classical Mechanics - xel02
http://mitpress.mit.edu/sicm/book.html
======
redsymbol
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-scmutil...](http://ai.redsymbol.net/2007/06/using-gnu-emacs-with-
scmutils.html)

~~~
neutronicus
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.

------
neutronicus
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"

~~~
ericlavigne
_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.

------
jules
> 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
_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>

_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
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".

------
namin
I once took the MIT class on which this book is based:
<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/>

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.

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

~~~
neutronicus
No, not at all. The first equation is an integral.

~~~
mechanical_fish
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
Wasn't the reason Newton invented calculus so that he could calculate
mechanics (i.e. Newton's Laws)?

~~~
zeynel1
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

------
realitygrill
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.

