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