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Got two accelerometers that are measuring accelerations oriented at +/- 45 deg from horizontal. I am looking to determine the conversion of the accelerometer measured data to accelerations in the vertical and horizontal direction. Can I use coordinate system conversion below ?

$$F_{Vertical} = (F_1 + F_2) \cos(\frac{\pi}{4})$$

$$F_{Horizontal} = (F_1 - F_2) \cos (\frac{\pi}{4})$$ enter image description here

I don't know phase relationship, but I can assume they are out of phase since I know the vertical acceleration is high and the horizontal acceleration is small.

Are the conversions above correct ?

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  • $\begingroup$ seems correct.... $\endgroup$
    – Vineet Menon
    Commented Nov 3, 2011 at 7:20
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    $\begingroup$ yes, it's just a rotation of a vector by 45 degrees. Note that $\cos 45$ degrees is equal to $1/\sqrt{2}$. $\endgroup$
    – Luboš Motl
    Commented Nov 3, 2011 at 10:19

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Accelerations can be treated as vectors, and therefore can be de-composed and rearranged (as in taking the horizontal and vertical components as you have done) as you like, provided you do the maths right!

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