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Euler angle sequences
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(Definition)
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"Euler angle sequences" is owned by bloftin.
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| Other names: |
"Euler angle rotation matrix", "Euler Angle Sequence" |
Cross-references: Euler 323 sequence, Euler 313 sequence, Euler 321 sequence, Euler 312 Sequence, Euler 232 sequence, Euler 212 sequence, Euler 231 sequence, Euler 213 sequence, Euler 131 sequence, Euler 121 sequence, Euler 132 Sequence, Euler 123 sequence, parameters, matrix
There are 15 references to this object.
This is version 6 of Euler angle sequences, born on 2005-08-19, modified 2026-02-16.
Object id is 71, canonical name is EulerAngles.
Accessed 114 times total.
Classification:
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Pending Errata and Addenda
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![$R_3(\psi)R_2(\theta)R_1(\phi) = \left[ \begin{array}{ccc} c_{\psi} c_{\theta} &... ... s_{\theta} & -c_{\theta} s_{\phi} & c_{\theta} c_{\phi} \end{array} \right] $](https://images.physicslibrary.org/cache/objects/71/l2h/img4.png "$R_3(\psi)R_2(\theta)R_1(\phi) = \left[ \begin{array}{ccc} c_{\psi} c_{\theta} &... ... s_{\theta} & -c_{\theta} s_{\phi} & c_{\theta} c_{\phi} \end{array} \right] $")
![$R_2(\psi)R_3(\theta)R_1(\phi) = \left[ \begin{array}{ccc} c_{\psi} c_{\theta} &... ..._{\phi} & s_{\psi} s_{\theta} s_{\phi} + c_{\psi} c_{\phi} \end{array} \right] $](https://images.physicslibrary.org/cache/objects/71/l2h/img5.png "$R_2(\psi)R_3(\theta)R_1(\phi) = \left[ \begin{array}{ccc} c_{\psi} c_{\theta} &... ..._{\phi} & s_{\psi} s_{\theta} s_{\phi} + c_{\psi} c_{\phi} \end{array} \right] $")
![$R_1(\psi)R_2(\theta)R_1(\phi) = \left[ \begin{array}{ccc} c_{\theta} & -s_{\the... ...{\phi} & -s_{\psi} s_{\phi} + c_{\psi} c_{\theta} c_{\phi} \end{array} \right] $](https://images.physicslibrary.org/cache/objects/71/l2h/img6.png "$R_1(\psi)R_2(\theta)R_1(\phi) = \left[ \begin{array}{ccc} c_{\theta} & -s_{\the... ...{\phi} & -s_{\psi} s_{\phi} + c_{\psi} c_{\theta} c_{\phi} \end{array} \right] $")
![$R_1(\psi)R_3(\theta)R_1(\phi) = \left[ \begin{array}{ccc} c_{\theta} & s_{\thet... ...\phi} & - s_{\psi} c_{\theta} s_{\phi} + c_{\psi} c_{\phi} \end{array} \right] $](https://images.physicslibrary.org/cache/objects/71/l2h/img7.png "$R_1(\psi)R_3(\theta)R_1(\phi) = \left[ \begin{array}{ccc} c_{\theta} & s_{\thet... ...\phi} & - s_{\psi} c_{\theta} s_{\phi} + c_{\psi} c_{\phi} \end{array} \right] $")
![$R_3(\psi)R_1(\theta)R_2(\phi) = \left[ \begin{array}{ccc} c_{\psi} c_{\phi} + s... ... c_{\theta} s_{\phi} & -s_{\theta} & c_{\theta} c_{\phi} \end{array} \right] $](https://images.physicslibrary.org/cache/objects/71/l2h/img8.png "$R_3(\psi)R_1(\theta)R_2(\phi) = \left[ \begin{array}{ccc} c_{\psi} c_{\phi} + s... ... c_{\theta} s_{\phi} & -s_{\theta} & c_{\theta} c_{\phi} \end{array} \right] $")
![$R_1(\psi)R_3(\theta)R_2(\phi) = \left[ \begin{array}{ccc} c_{\theta} c_{\phi} &... ...\theta} & -s_{\psi} s_{\theta} s_{\phi} +c_{\psi} c_{\phi} \end{array} \right] $](https://images.physicslibrary.org/cache/objects/71/l2h/img9.png "$R_1(\psi)R_3(\theta)R_2(\phi) = \left[ \begin{array}{ccc} c_{\theta} c_{\phi} &... ...\theta} & -s_{\psi} s_{\theta} s_{\phi} +c_{\psi} c_{\phi} \end{array} \right] $")
![$R_2(\psi)R_1(\theta)R_2(\phi) = \left[ \begin{array}{ccc} c_{\psi} c_{\phi} - s... ...theta} & -s_{\psi} s_{\phi} + c_{\psi} c_{\theta} c_{\phi} \end{array} \right] $](https://images.physicslibrary.org/cache/objects/71/l2h/img10.png "$R_2(\psi)R_1(\theta)R_2(\phi) = \left[ \begin{array}{ccc} c_{\psi} c_{\phi} - s... ...theta} & -s_{\psi} s_{\phi} + c_{\psi} c_{\theta} c_{\phi} \end{array} \right] $")
![$R_2(\psi)R_3(\theta)R_2(\phi) = \left[ \begin{array}{ccc} c_{\psi} c_{\theta} c... ...heta} & - s_{\psi} c_{\theta} s_{\phi} + c_{\psi} c_{\phi} \end{array} \right] $](https://images.physicslibrary.org/cache/objects/71/l2h/img11.png "$R_2(\psi)R_3(\theta)R_2(\phi) = \left[ \begin{array}{ccc} c_{\psi} c_{\theta} c... ...heta} & - s_{\psi} c_{\theta} s_{\phi} + c_{\psi} c_{\phi} \end{array} \right] $")
![$R_2(\psi)R_1(\theta)R_3(\phi) = \left[ \begin{array}{ccc} c_{\psi} c_{\phi} - s... ...\phi} - c_{\psi} s_{\theta} c_{\phi} & c_{\psi} c_{\theta} \end{array} \right] $](https://images.physicslibrary.org/cache/objects/71/l2h/img12.png "$R_2(\psi)R_1(\theta)R_3(\phi) = \left[ \begin{array}{ccc} c_{\psi} c_{\phi} - s... ...\phi} - c_{\psi} s_{\theta} c_{\phi} & c_{\psi} c_{\theta} \end{array} \right] $")
![$R_1(\psi)R_2(\theta)R_3(\phi) = \left[ \begin{array}{ccc} c_{\theta} c_{\phi} &... ...\phi} + c_{\psi} s_{\theta} s_{\phi} & c_{\psi} c_{\theta} \end{array} \right] $](https://images.physicslibrary.org/cache/objects/71/l2h/img13.png "$R_1(\psi)R_2(\theta)R_3(\phi) = \left[ \begin{array}{ccc} c_{\theta} c_{\phi} &... ...\phi} + c_{\psi} s_{\theta} s_{\phi} & c_{\psi} c_{\theta} \end{array} \right] $")
![$R_3(\psi)R_1(\theta)R_3(\phi) = \left[ \begin{array}{ccc} c_{\psi} c_{\phi} - s... ... s_{\theta} s_{\phi} & -s_{\theta} c_{\phi} & c_{\theta} \end{array} \right] $](https://images.physicslibrary.org/cache/objects/71/l2h/img14.png "$R_3(\psi)R_1(\theta)R_3(\phi) = \left[ \begin{array}{ccc} c_{\psi} c_{\phi} - s... ... s_{\theta} s_{\phi} & -s_{\theta} c_{\phi} & c_{\theta} \end{array} \right] $")
![$R_3(\psi)R_2(\theta)R_3(\phi) = \left[ \begin{array}{ccc} c_{\psi} c_{\theta} c... ...\ s_{\theta} c_{\phi} & s_{\theta} s_{\phi} & c_{\theta} \end{array} \right] $](https://images.physicslibrary.org/cache/objects/71/l2h/img15.png "$R_3(\psi)R_2(\theta)R_3(\phi) = \left[ \begin{array}{ccc} c_{\psi} c_{\theta} c... ...\ s_{\theta} c_{\phi} & s_{\theta} s_{\phi} & c_{\theta} \end{array} \right] $")