chaosbook:billiards

(ChaosBook.org blog, chapter Billiards) — *Predrag Cvitanovic 2009-02-11 12:55*

Now go forth and play billiards — *John F. Gibson, 2009-02-12 17:27 *

**Mason A Porter 2010-02-14**
I'm going through this because I am writing up a solution to a problem that follows this derivation. I have asked my students to derive the Jacobian for billiards in problem 7 of homework 3, which is on maps, in my class. The website for the class is nonlinear2010.blogspot.com

**Predrag 2010-02-14**
Great. The chapter needs some loving care, formulas like those of Example 8.1 (3-disks) are a bit stupid. Please use my internal version, perhaps more useful for this purpose. Students should also understand the next chapter, “World in a mirror,” doing dynamics on the fundamental domain is much smarter than dynamics without desymmetrization. Good problems and solutions we could add to ChaosBook exercises/solutions.

**Mason A Porter 2010-02-14**
Immediately in line below equation (8.6):
You are missing two “^+” superscripts.
**Predrag 2010-02-14** I made the editorial decision to mark only “^-” superscripts. If you think it is confusing, I can add throughout “^+” superscripts, but it ain't pretty…

**Mason A Porter 2010-02-14**
In equ (8.11), it should be *k = 1* in the bottom and *n_p* on top (unless you are purposely going against that convention).
**Predrag 2010-02-14** Otherwise one would be tempted to multiply the wrong way. Now I say “The unconventional product limits are a reminder that
the product is time-ordered, with later times corresponding to
multiplication from the left, as in (4.52), AKA equ label {jacoB}.”

**Mason A Porter 2010-02-14**
You switch back and forth regarding *k*th and *n*th collisions and it would be better to be uniform.
**Predrag 2010-02-14**
Historical - cycle length is *n* so sums up *n* were labeled by *k*. But I can see it is not necessary - fixed now.

**Mason A Porter 2010-02-14**
You refer to a “velocity” of 1 rather than a “speed” of 1 on several occasions.
**Predrag 2010-02-14** thanks, fixed.

~~DISCUSSION~~

chaosbook/billiards.txt · Last modified: 2010/02/14 15:19 by predrag