<- [[:chaosbook]] ====== Chapter: Billiards ====== (ChaosBook.org blog, chapter [[http://chaosbook.org/paper.shtml#billiards|Billiards]]) --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-02-11 12:55// Now go forth and play billiards --- //John F. Gibson, 2009-02-12 17:27 // ===== Proofreading, to implement ===== **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 [[http://nonlinear2010.blogspot.com/|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 [[http://chaosbook.org/old/billiards.pdf|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}." ===== Proofreading, implemented ===== **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~~