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call them, the axis can be external to the rotating axis, like a rocket spinning along it's length, but spun on a stick at some other direction is an external rotation, or the rotation really happens from outside the rotating frame. The other is the thrusters on the rocket itself that are generating a torque, and their applied rotation to the rocket's rotation changes as the rocket rotates, and is internal to the frame, or part of the frame of the rocket. The difference between the two is the direction of the cross product in the
Rodrigues Forumla.
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936:{\displaystyle {\begin{array}{lcl}\mathbf {A} &=&{\begin{bmatrix}\cos \theta \cos \psi &\cos \phi \sin \psi +\sin \phi \sin \theta \cos \psi &\sin \phi \sin \psi -\cos \phi \sin \theta \cos \psi \\-\cos \theta \sin \psi &\cos \phi \cos \psi -\sin \phi \sin \theta \sin \psi &\sin \phi \cos \psi +\cos \phi \sin \theta \sin \psi \\\sin \theta &-\sin \phi \cos \theta &\cos \phi \cos \theta \\\end{bmatrix}}\end{array}}}
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1160:, because the so-called rotation vector (properly a bivector) is the logarithm of a rotor ("unit quaternion"). We could add some text somewhere discussing the logarithm of a rotor or a rotation matrix, but duplicating a bunch of formulas into two different sections of the article in an expansive, completely unsourced formulary is just confusing to readers. –
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this doesn't look like R3; or 3 real numbers. This is meant to be Euler Axis to Euler Axis; there's two operations, to rotate a point around the axis, and to rotate a Euler Axis around a Euler Axis. But additionally, the rotation of a rotation can either be intrinsic or extrinsic (That's what I
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Euler Axis is additive, in the context that the various torques generated by engines expressed as Euler Axis (angle*axis resolved) can just be added together. Rotations that happen at the same time to a thing are additive; and with subtraction you can find the missing axis-angle you would have
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You are right. I already twice draw attention to the fact that this article is partially false , but without success . It should be coordinated with the Euler angles article. That is a lot of work and I will not begin it without support from other editors involved.
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within that same section. Indeed, the article mentions rotating around zxz for the first formula, and rotating around xyz for the second formula. Indeed, you can see the two formulas can't be consistent for the first formula claims that
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579:{\displaystyle {\begin{aligned}\phi &=\operatorname {arctan2} (A_{31},A_{32})\\\theta &=\arccos(A_{33})\\\psi &=-\operatorname {arctan2} (A_{13},A_{23})\end{aligned}}}
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additionally needed to get to where you are that you didn't have... But it should be an extra article maybe? With
Original Research Tagged on it?
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I'm having a lot of trouble understanding what you are trying to say. Do you have a source which elaborates, e.g. a published paper somewhere? –
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is there any hope to save the article? Can we collaborate to get those few formula integrated with the rest of the article?
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Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
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Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
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describes how to compute Euler angles of a rotation from the rotation matrix. The formulas in that section use
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Could you figure out the correct formulas for a single convention and fix the article? Thanks in advance.
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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Formula to compute Euler angles from matrix uses two different conventions
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can just be deleted. It doesn't say anything independently interesting. –
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The matrix above is for left-hand system, not right-hand.
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I have this original copy, minus a few minor edits...
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I just deleted the "Angle-angle-angle" section, which
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Again, I think the article I mentioned above is OK .
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