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x
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x
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raw accelerometer reading in the x axis
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y
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y
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raw accelerometer reading in the y axis
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z
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z
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raw accelerometer reading in the z axis
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rxyz
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\( \left\Vert \begin{array}{c}x\\ {}y\\ {}z\end{array}\right\Vert \)
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magnitude of resultant vector
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rxy
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\( \left\Vert \begin{array}{c}x\\ {}y\end{array}\right\Vert \)
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magnitude of resultant vector in x,y plane
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rxz
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\( \left\Vert \begin{array}{c}x\\ {}z\end{array}\right\Vert \)
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magnitude of resultant vector in x,z plane
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ryz
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\( \left\Vert \begin{array}{c}y\\ {}z\end{array}\right\Vert \)
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magnitude of resultant vector in y,z plane
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ϑxy
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\( \arctan \left(\frac{y}{x}\right) \)
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angle of resultant vector in x,y plane
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ϑxz
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\( \arctan \left(\frac{z}{x}\right) \)
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angle of resultant vector in x,z plane
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ϑyz
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\( \arctan \left(\frac{z}{y}\right) \)
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angle of resultant vector in y,z plane
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ϑz
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\( \arctan \left(\frac{z}{\left\Vert \begin{array}{c}x\\ {}y\end{array}\right\Vert}\right) \)
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angle of resultant vector with x,y plane collapsed to 1 line
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ϑy
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\( \arctan \left(\frac{y}{\left\Vert \begin{array}{c}x\\ {}z\end{array}\right\Vert}\right) \)
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angle of resultant vector with x,z plane collapsed to 1 line
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ϑx
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\( \arctan \left(\frac{x}{\left\Vert \begin{array}{c}y\\ {}z\end{array}\right\Vert}\right) \)
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angle of resultant vector with y,z plane collapsed to 1 line
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Ωx
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\( \arcsin \left(\frac{yz}{\left\Vert \begin{array}{c}x\\ {}y\\ {}0\end{array}\left\Vert \begin{array}{c}\\ {}\\ {}\end{array}\right\Vert \begin{array}{c}x\\ {}0\\ {}z\end{array}\right\Vert}\right) \)
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solid angle of resultant pyramid base projected along x axis
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Ωy
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\( \arcsin \left(\frac{xz}{\left\Vert \begin{array}{c}x\\ {}y\\ {}0\end{array}\left\Vert \begin{array}{c}\\ {}\\ {}\end{array}\right\Vert \begin{array}{c}0\\ {}y\\ {}z\end{array}\right\Vert}\right) \)
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solid angle of resultant pyramid base projected along y axis
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Ωz
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\( \arcsin \left(\frac{xy}{\left\Vert \begin{array}{c}x\\ {}0\\ {}z\end{array}\left\Vert \begin{array}{c}\\ {}\\ {}\end{array}\right\Vert \begin{array}{c}0\\ {}y\\ {}z\end{array}\right\Vert}\right) \)
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solid angle of resultant pyramid base projected along z axis
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Vxyz
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xyz
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volume of resultant cuboid
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Ax
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yz
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area of resultant pyramid base projected along x axis
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Ay
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xz
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area of resultant pyramid base projected along y axis
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Az
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xy
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area of resultant pyramid base projected along z axis
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Axyz
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\( \frac{1}{2}\left\Vert \left[\begin{array}{c}x\\ {}y\\ {}0\end{array}\right]\times \left[\begin{array}{c}x\\ {}0\\ {}z\end{array}\right]\right\Vert \)
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area of resultant triangle
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