"곡면 위의 측지선"의 두 판 사이의 차이

2012년 6월 20일 (수) 10:35 판

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
\(\dot{s}=p_{s}\)
\(\dot{\theta}=\frac{1}{f(s)^2}p_{\theta}\)
\(\dot{p_s}=\frac{f'(s)}{f(s)^3}p_{\theta}^2\)
\(\dot{p_{\theta}}=0\)

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

Jacobi’s geodesic flow on an ellipsoid
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.
Knörrer, Horst. 1980. Geodesics on the ellipsoid. Inventiones Mathematicae 59, no. 2 (6): 119-143. doi: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:10.1016/j.geomphys.2007.07.006. http://arxiv.org/abs/math-ph/0609073.

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-*  1838 Ja<br>
+*  1838 Jacobi<br>
+*  1979 Moser<br>
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+*  J. Moser, Geometry of quadrics and spectral theory, Chern Sympos., Springer-Verlag 1980, pp. 147-188<br>
 *  Jacobi’s geodesic flow on an ellipsoid<br>
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 * http://ko.wikipedia.org/wiki/
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