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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Perifocal coordinate system ： ウィキペディア英語版 Perifocal coordinate system The perifocal coordinate (PQW) system is a frame of reference for an orbit. The frame is centered at the focus of the orbit, i.e. the celestial body about which the orbit is centered. The unit vectors $\backslash bold\}$ lie in the plane of the orbit. $\backslash bold\}$ has a true anomaly ($\backslash theta$) of 90 degrees past the periapsis. The third unit vector $\backslash bold\}\; =\; \backslash bold\}$ And, since $\backslash bold\}\; =\; \backslash frac\backslash |\}$ Where h is the specific relative angular momentum. The position and velocity vectors can be determined for any location of the orbit. The position vector, r, can be expressed as: :$\backslash bold\; =\; \backslash |r\backslash |\; \backslash cos\; \backslash theta\; \backslash mathbf\}$ Where $\backslash theta$ is the true anomaly and the radius ''r'' may be calculated from the orbit equation. The velocity vector, v, is found by taking the time derivative of the position vector: :$\backslash bold\; =\; \backslash bold\; \backslash cos\; \backslash theta\; -\; r\; \backslash dot\; \backslash sin\; \backslash theta)\backslash bold\; \backslash sin\; \backslash theta\; +\; r\; \backslash dot\; \backslash cos\; \backslash theta)\backslash bold\; =\; \backslash frace\; \backslash sin\; \backslash theta$ where $\backslash mu$ is the gravitational parameter of the focus, ''h'' is the specific relative angular momentum of the orbital body, ''e'' is the eccentricity of the orbit, and $\backslash theta$ is the true anomaly. $\backslash dot$ is the radial component of the velocity vector (pointing inward toward the focus) and $r\; \backslash dot$ is the tangential component of the velocity vector. By substituting the equations for $\backslash dot$ and $r\; \backslash dot$ into the velocity vector equation and simplifying, the final form of the velocity vector equation is obtained as:〔Curtis, H. D. (2005). ''Orbital Mechanics for Engineering Students.'' Burlington, MA: Elsevier Buttersorth-Heinemann. pp 76–77〕 :$\backslash bold\; =\; \backslash frac(\backslash theta\; \backslash bold\})$ ==Transformation from equatorial coordinate system== The perifocal coordinate system can also be defined using the orbital parameters inclination (''i''), right ascension ($\backslash Omega$) and the argument of perigee ($\backslash omega$). The following equations transform an orbit from the equatorial coordinate system to the perifocal coordinate system.〔Snow, K. (1999). ''Orbits in Space.''〕 :$$ \begin p_i & = \cos \Omega \cos \omega - \sin \Omega \cos i \sin \omega \\ p_j & = \sin \Omega \cos \omega + \cos \Omega \cos i \sin \omega \\ p_k & = \sin i \sin \omega \\() q_i & = -\cos \Omega \sin \omega - \sin \Omega \cos i \cos \omega \\ q_j & = -\sin \Omega \sin \omega + \cos \Omega \cos i \cos \omega \\ q_k & = \sin i \cos \omega \\() w_i & = \sin i \sin \Omega \\ w_j & = -\sin i \cos \Omega \\ w_k & = \cos i \end where :$$ \begin \bold} + p_j\bold} \\ \bold} + q_j\bold} \\ \bold} + w_j\bold} \end and $\backslash bold\}$, and $\backslash bold\{\backslash hat\{K\}\}$ are the unit vectors of the equatorial coordinate system. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Perifocal coordinate system」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.