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chaosbook:billiards [2010/02/02 07:55]
127.0.0.1 external edit
chaosbook:billiards [2010/02/14 15:19] (current)
predrag Mason's Billiards chapter comments
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 (ChaosBook.org blog, chapter [[http://​chaosbook.org/​paper.shtml#​billiards|Billiards]]) ​ --- //​[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-02-11 12:55// (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 //
  
-created ​billiards ​thread ​for testing+===== 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.
  
-now go forth and play billiards --- //John F. Gibson, 2009-02-12 17:27 // 
  
 ~~DISCUSSION~~ ~~DISCUSSION~~
  
chaosbook/billiards.txt · Last modified: 2010/02/14 15:19 by predrag