# Rotation of Gyroscopic Sensor, Euler Angles

TLDR: What relationship exists between my Euler and my rotations about each axis all sampled at the same time..

Background: So I have a few outputs from a sensor, the angular speed about the x,y,z axis as well as a time stamp. So I'm estimating the rotation about each as (angular velocity about the axis)* (time between measurements). I have an acceleration vector in this three space that I want to rotate, based on the angles described by the step above, so I want to feed this vector into a rotation matrix like this one...

Question: So does my rotation About X, About Y, and About Z correspond to the Euler angles, or is there an easier form of the rotation matrix for just this purpose?

## 1 Answer

They don't correspond directly to Euler angles. Which is a good thing anyway, because Euler angles are a rubbish way of handling general rotations. A better representation would be quaternions, and I think your rotations about each axis x, y, z should correspond directly to i, j, k in the quaternion representation. https://en.wikipedia.org/wiki/Quaternion

The angular velocity times the time between measurements will give you the change in orientation, but don't rely on this as an estimate of the current orientation, because errors accumulate and you'll find it becomes incorrect very quickly.