chaosbook:billiards
====== Differences ====== This shows you the differences between two versions of the page.
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chaosbook:billiards [2009/02/12 17:25] wikiadmin created |
chaosbook:billiards [2010/02/14 15:19] (current) predrag Mason's Billiards chapter comments |
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| - | ====== Billiards ====== | + | ====== Chapter: Billiards ====== |
| - | //John F. Gibson, 2009-02-12 17:24 // | + | (ChaosBook.org blog, chapter [[http://chaosbook.org/paper.shtml#billiards|Billiards]]) --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-02-11 12:55// |
| - | made a billiards page, for testing purposes | + | Now go forth and play billiards --- //John F. Gibson, 2009-02-12 17:27 // |
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| + | ===== Proofreading, to implement ===== | ||
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| + | **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]] | ||
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| + | **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. | ||
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| + | **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... | ||
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| + | **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}." | ||
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| + | ===== Proofreading, implemented ===== | ||
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| + | **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. | ||
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| + | **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 | ||
| ~~DISCUSSION~~ | ~~DISCUSSION~~ | ||
chaosbook/billiards.1234488313.txt.gz · Last modified: 2009/02/12 17:25 by wikiadmin
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