"곡면 위의 측지선"의 두 판 사이의 차이

수학노트
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(사용자 2명의 중간 판 11개는 보이지 않습니다)
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==개요==
  
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* [[곡면 위의 측지선]]<br>
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* 매개곡선 <math>(f(s),0,g(s))</math>을 z-축을 중심으로 회전시켜 얻어지는 곡면 <math>(f(s)\cos\theta,f(s)\sin\theta,g(s))</math>
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* <math>p_s</math>는 s의 conjugate variable
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* <math>p_\theta</math>는 <math>\theta</math>의 conjugate variable
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*  해밀토니안:<math>H((s,\theta),(p_s,p_{\theta}))=\frac{1}{2}(p_s^2+\frac{1}{f(s)^2}p_{\theta}^2)</math>
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*  운동방정식:<math>\dot{s}=p_{s}</math>:<math>\dot{\theta}=\frac{1}{f(s)^2}p_{\theta}</math>:<math>\dot{p_s}=\frac{f'(s)}{f(s)^3}p_{\theta}^2</math>:<math>\dot{p_{\theta}}=0</math>
  
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==역사==
  
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*  매개곡선 <math>(f(s),0,g(s))</math>을 z-축을 중심으로 회전시켜 얻어지는 곡면 <math>(f(s)\cos\theta,f(s)\sin\theta,g(s))</math><br>
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*  1838 Jacobi
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* <math>p_s</math>는 s의 conjugate variable<br>
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* 1979 Moser
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* <math>p_\theta</math>는 <math>\theta</math>의 conjugate variable<br>
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* http://www.google.com/search?hl=en&tbs=tl:1&q=
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*  해밀토니안<br><math>H((s,\theta),(p_s,p_{\theta}))=\frac{1}{2}(p_s^2+\frac{1}{f(s)^2}p_{\theta}^2)</math><br>
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* 
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*  운동방정식<br><math>\dot{s}=p_{s}</math><br><math>\dot{\theta}=\frac{1}{f(s)^2}p_{\theta}</math><br><math>\dot{p_s}=\frac{f'(s)}{f(s)^3}p_{\theta}^2</math><br><math>\dot{p_{\theta}}=0</math><br>
 
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* 1838 Ja<br>
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* http://www.google.com/search?hl=en&tbs=tl:1&q=
 
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==메모==
  
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*  J. Moser, Geometry of quadrics and spectral theory, Chern Sympos., Springer-Verlag 1980, pp. 147-188
  
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*  Jacobi’s geodesic flow on an ellipsoid
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*  Jacobi’s geodesic flow on an ellipsoid<br>
 
 
* S. L. Tabachnikov, “Ellipsoids, complete integrability and hyperbolic geometry”, Mosc. Math. J., 2:1 (2002), 183–196 http://goo.gl/feeiG
 
* S. L. Tabachnikov, “Ellipsoids, complete integrability and hyperbolic geometry”, Mosc. Math. J., 2:1 (2002), 183–196 http://goo.gl/feeiG
 
* Anon.n.d. ACTION INTEGRALS FOR ELLIPSOIDAL BILLIARDS. Text. http://cat.inist.fr/?aModele=afficheN&cpsidt=11135284.
 
* Anon.n.d. ACTION INTEGRALS FOR ELLIPSOIDAL BILLIARDS. Text. http://cat.inist.fr/?aModele=afficheN&cpsidt=11135284.
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* Knörrer, Horst. 1980. Geodesics on the ellipsoid. Inventiones Mathematicae 59, no. 2 (6): 119-143. doi:[http://dx.doi.org/10.1007/BF01390041 10.1007/BF01390041]. 
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* Knörrer, Horst. 1980. Geodesics on the ellipsoid. Inventiones Mathematicae 59, no. 2 (6): 119-143. doi:[http://dx.doi.org/10.1007/BF01390041 10.1007/BF01390041].  
 
* Davison, Chris M, Holger R Dullin, and Alexey V Bolsinov. 2006. Geodesics on the Ellipsoid and Monodromy. math-ph/0609073 (September 26). doi:doi:[http://dx.doi.org/10.1016/j.geomphys.2007.07.006 10.1016/j.geomphys.2007.07.006]. http://arxiv.org/abs/math-ph/0609073.
 
* Davison, Chris M, Holger R Dullin, and Alexey V Bolsinov. 2006. Geodesics on the Ellipsoid and Monodromy. math-ph/0609073 (September 26). doi:doi:[http://dx.doi.org/10.1016/j.geomphys.2007.07.006 10.1016/j.geomphys.2007.07.006]. http://arxiv.org/abs/math-ph/0609073.
  
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==관련된 항목들==
  
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<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">물리학용어번역</h5>
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==물리학용어번역==
  
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* 단어사전 http://www.google.com/dictionary?langpair=en|ko&q=
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* 단어사전 http://www.google.com/dictionary?langpair=en|ko&q=
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* 발음사전 http://www.forvo.com/search/
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* 발음사전 http://www.forvo.com/search/
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*  한국물리학회 물리용어<br>
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*  한국물리학회 물리용어
 
** http://www.kps.or.kr/home/kor/morgue/dic/default.asp?globalmenu=6&localmenu=2
 
** http://www.kps.or.kr/home/kor/morgue/dic/default.asp?globalmenu=6&localmenu=2
 
** http://www.kps.or.kr/home/kor/morgue/dic/word_list.asp?globalmenu=6&localmenu=2&lang=english
 
** http://www.kps.or.kr/home/kor/morgue/dic/word_list.asp?globalmenu=6&localmenu=2&lang=english
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* [http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집]<br>
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* [http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집]
 
** http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr=
 
** http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr=
 
* [http://www.nktech.net/science/term/term_l.jsp?l_mode=cate&s_code_cd=MA 남·북한수학용어비교]
 
* [http://www.nktech.net/science/term/term_l.jsp?l_mode=cate&s_code_cd=MA 남·북한수학용어비교]
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* [http://kms.or.kr/home/kor/board/bulletin_list_subject.asp?bulletinid=%7BD6048897-56F9-43D7-8BB6-50B362D1243A%7D&boardname=%BC%F6%C7%D0%BF%EB%BE%EE%C5%E4%B7%D0%B9%E6&globalmenu=7&localmenu=4 대한수학회 수학용어한글화 게시판]
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* [http://kms.or.kr/home/kor/board/bulletin_list_subject.asp?bulletinid=%7BD6048897-56F9-43D7-8BB6-50B362D1243A%7D&boardname=%BC%F6%C7%D0%BF%EB%BE%EE%C5%E4%B7%D0%B9%E6&globalmenu=7&localmenu=4 대한수학회 수학용어한글화 게시판]
  
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<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">사전 형태의 자료</h5>
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==사전 형태의 자료==
  
 
* http://ko.wikipedia.org/wiki/
 
* http://ko.wikipedia.org/wiki/
 
* http://en.wikipedia.org/wiki/
 
* http://en.wikipedia.org/wiki/
  
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<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">관련논문</h5>
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* http://www.jstor.org/action/doBasicSearch?Query=
 
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* http://www.ams.org/mathscinet
 
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* http://dx.doi.org/
 
  
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<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">관련도서</h5>
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*  도서내검색<br>
 
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** http://books.google.com/books?q=
 
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** http://book.daum.net/search/contentSearch.do?query=
 
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*  도서검색<br>
 
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** http://books.google.com/books?q=
 
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** http://book.daum.net/search/mainSearch.do?query=
 
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** http://book.daum.net/search/mainSearch.do?query=
 
  
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<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">블로그</h5>
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==블로그==
  
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*  구글 블로그 검색<br>
 
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** http://blogsearch.google.com/blogsearch?q=
 
 
** http://blogsearch.google.com/blogsearch?q=
 
** http://blogsearch.google.com/blogsearch?q=
 
* 기타
 
* 기타
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[[분류:적분가능모형]]
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[[분류:수리물리학]]

2020년 12월 28일 (월) 02:04 기준 최신판

개요

  • 매개곡선 \((f(s),0,g(s))\)을 z-축을 중심으로 회전시켜 얻어지는 곡면 \((f(s)\cos\theta,f(s)\sin\theta,g(s))\)
  • \(p_s\)는 s의 conjugate variable
  • \(p_\theta\)는 \(\theta\)의 conjugate variable
  • 해밀토니안\[H((s,\theta),(p_s,p_{\theta}))=\frac{1}{2}(p_s^2+\frac{1}{f(s)^2}p_{\theta}^2)\]
  • 운동방정식\[\dot{s}=p_{s}\]\[\dot{\theta}=\frac{1}{f(s)^2}p_{\theta}\]\[\dot{p_s}=\frac{f'(s)}{f(s)^3}p_{\theta}^2\]\[\dot{p_{\theta}}=0\]



역사



메모

  • J. Moser, Geometry of quadrics and spectral theory, Chern Sympos., Springer-Verlag 1980, pp. 147-188



관련된 항목들

물리학용어번역



사전 형태의 자료










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