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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 Eigenvector slew ： ウィキペディア英語版 Eigenvector slew In aerospace engineering, especially those areas dealing with spacecraft, the eigenvector slew is a method to calculate a steering correction (called a slew) by rotating the spacecraft around one fixed axis. This corresponds in general to the fastest and most efficient way to reach the desired target orientation as there is only one acceleration phase and one braking phase for the angular rate. If this fixed axis is not a principal axis a time varying torque must be applied to force the spacecraft to rotate as desired, though. Also the gyroscopic effect of momentum wheels must be compensated for. That such a rotation exists corresponds precisely to a main result of the mathematical theory of rotation operators, the (only real) eigenvector of the rotation operator corresponding to the desired re-orientation is this axis. Given the current orientation of the craft, and the desired orientation of the craft in cartesian coordinates, the required axis of rotation and corresponding rotation angle to achieve the new orientation is determined by computing the eigenvector of the rotation operator. == Problem == Let :$\backslash hat\backslash \; ,\backslash \; \backslash hat\backslash \; ,\backslash \; \backslash hat$ be a body fixed reference system for a 3 axis stabilized spacecraft. The initial attitude is given by :$\backslash hat=\backslash hat$ :$\backslash hat=\backslash hat$ :$\backslash hat=\backslash hat.$ One wants to find an axis relative the spacecraft body :$\backslash hat=r\_x\; \backslash cdot\; \backslash hat\; +r\_y\; \backslash cdot\; \backslash hat\; +r\_z\; \backslash cdot\; \backslash hat$ and a rotation angle $\backslash alpha$ such that after the rotation with the angle $\backslash alpha$ one has that :$\backslash hat=\backslash hat$ :$\backslash hat=\backslash hat$ :$\backslash hat=\backslash hat$ where :$\backslash hat\backslash \; ,\backslash \; \backslash hat\backslash \; ,\backslash \; \backslash hat$ are the new target directions. In vector form this means that :$\backslash hat=r\_a\; \backslash cdot\; \backslash hat\; +\; \backslash cos\; \backslash alpha\; \backslash cdot\; (\; \backslash hat\; -\; r\_a\; \backslash cdot\; \backslash hat)+$ \sin \alpha \cdot \hat \times \hat :$\backslash hat=r\_b\; \backslash cdot\; \backslash hat\; +\; \backslash cos\; \backslash alpha\; \backslash cdot\; (\; \backslash hat\; -\; r\_b\; \backslash cdot\; \backslash hat)+$ \sin \alpha \cdot \hat \times \hat :$\backslash hat=r\_c\; \backslash cdot\; \backslash hat\; +\; \backslash cos\; \backslash alpha\; \backslash cdot\; (\; \backslash hat\; -\; r\_c\; \backslash cdot\; \backslash hat)+$ \sin \alpha \cdot \hat \times \hat. 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「Eigenvector slew」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.