구면좌표계
이 항목의 스프링노트 원문주소
개요
- \(\rho ,\phi ,\theta\)
- \(x=\rho \cos\phi \, \sin\theta\)
- \(y=\rho \sin\phi \, \sin\theta\)
- \(z=\rho \cos\theta\)
- \(0<\phi<2\pi\), \(0<\theta<\pi\)
메트릭 텐서
\(\left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & \rho ^2 \sin ^2(\theta ) & 0 \\ 0 & 0 & \rho ^2 \end{array} \right)\)
라플라시안
- 라플라시안
\(\Delta f = {1 \over r^2} {\partial \over \partial r} \left( r^2 {\partial f \over \partial r} \right) + {1 \over r^2 \sin \theta} {\partial \over \partial \theta} \left( \sin \theta {\partial f \over \partial \theta} \right) + {1 \over r^2 \sin^2 \theta} {\partial^2 f \over \partial \phi^2}\)
크리스토펠 기호
- 크리스토펠 기호 항목 참조
\(\begin{array}{ll} \Gamma _{11}^1 & 0 \\ \Gamma _{12}^1 & 0 \\ \Gamma _{13}^1 & 0 \\ \Gamma _{21}^1 & 0 \\ \Gamma _{22}^1 & -\rho \sin ^2(\theta ) \\ \Gamma _{23}^1 & 0 \\ \Gamma _{31}^1 & 0 \\ \Gamma _{32}^1 & 0 \\ \Gamma _{33}^1 & -\rho \\ \Gamma _{11}^2 & 0 \\ \Gamma _{12}^2 & \frac{1}{\rho } \\ \Gamma _{13}^2 & 0 \\ \Gamma _{21}^2 & \frac{1}{\rho } \\ \Gamma _{22}^2 & 0 \\ \Gamma _{23}^2 & \cot (\theta ) \\ \Gamma _{31}^2 & 0 \\ \Gamma _{32}^2 & \cot (\theta ) \\ \Gamma _{33}^2 & 0 \\ \Gamma _{11}^3 & 0 \\ \Gamma _{12}^3 & 0 \\ \Gamma _{13}^3 & \frac{1}{\rho } \\ \Gamma _{21}^3 & 0 \\ \Gamma _{22}^3 & \sin (\theta ) (-\cos (\theta )) \\ \Gamma _{23}^3 & 0 \\ \Gamma _{31}^3 & \frac{1}{\rho } \\ \Gamma _{32}^3 & 0 \\ \Gamma _{33}^3 & 0 \end{array}\)
역사
메모
관련된 항목들
수학용어번역
사전 형태의 자료
- http://ko.wikipedia.org/wiki/구면좌표계
- http://en.wikipedia.org/wiki/Spherical_coordinates
- http://en.wikipedia.org/wiki/Polar_coordinate_system
- http://en.wikipedia.org/wiki/
- http://www.wolframalpha.com/input/?i=
- NIST Digital Library of Mathematical Functions
- The On-Line Encyclopedia of Integer Sequences
관련논문
관련도서 및 추천도서
- 도서내검색
- 도서검색
관련기사
- 네이버 뉴스 검색 (키워드 수정)