Math help request

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Falling Snow KumaMoto

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Post 2019.07.23 13:32

Math help request

I measured a vector, getting x, y, and z values in cartesian coordinates. I then had to use a program to process the data that did a great many things, including rotate the coordinate system (about all 3 axes), giving me u, v, and w values for the original measured vector in the new coordinate system. The program was helpful in other ways, but did not give me the rotation angles.

Now I need the angle between the new w axis and the old z axis.

Who knows how to do this?? I offer my gratitude plus a free HSC doctrine ship of your choice for whoever knows how to fix this!
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Titus Tallang

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Post 2019.07.23 16:42

Re: Math help request

The coordinate transformation you're trying to find is some linear permutation π on R³. Since you're interested in the vector in the original (cartesian) system that corresponds to the w axis of your new system, you are looking for π⁽⁻¹⁾(0,0,1).

To determine π⁽⁻¹⁾(0,0,1), you need measurements of π such that (0,0,1) can be expressed as some linear combination of the results. If you measure π at three linearly independent points in R³, you can ensure that this is the case.

Once you have your three measurements, make use the fact that π is linear:

(0,0,1) = α · π(p₁) + β · π(p₂) + γ · π(p₃)

π⁽⁻¹⁾(0,0,1) = α · p₁ + β · p₂ + γ · p₃.


Once you have obtained π⁽⁻¹⁾(0,0,1), normalize it, then take the arc cosine of its z coordinate to find the angle between it and the z axis.
Scientia potentia est.
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Falling Snow KumaMoto

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Post 2019.08.16 15:35

Re: Math help request

Thank you for the help! Having failed to understand what you wrote, I conclude you must be correct. :)

Which lovely HSC doctrine ship would you like? A lovely T2 BLAP Augoror? The uber-popular caracal?
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Troven Smalvard

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Post 2019.08.16 17:47

Re: Math help request

i didn't understand either, but i know your original spell must have been some arcane magic to summon forth the Titus from his slumber :)
with great power come great responsibility young Falling Snow, use it wisely






also

Hi Titus :happy3:
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Falling Snow KumaMoto

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Post 2019.08.16 20:23

Re: Math help request

Lol, Troven. :)

Long ago, I read this book about a magician who couldn't find a teacher, so he was hunting around ancient ruins and libraries looking for spells + techniques. He found one that would allow him to summon "the Eater of Heads". He declined to cast the spell.

My teen self was horrified that he kicked this power away, but his reason was that the papers did not specify how to designate whose heads would be eaten. It also lacked a clear means of telling the eater to stop eating and go away. I learned much from this passage, and it still makes me laugh 30 years later.
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