# Rotation of Angular Velocity with Gyroscopes

1. Apr 7, 2010

### wbp2105

1. The problem statement, all variables and given/known data

As part of a senior design project, I am trying to figure out the global orientation of a gyroscope (i.e. the three angles of rotation around the global X, Y, and Z axes to realign the local x, y, and z axes of the gyro with the global axes). The gyroscope gives the rotational velocity of the gyroscope around the three local axes. Originally, I just going to integrate the rotational velocities to get the angles, but I think that this will not work because the axes are also rotating (as the gyro rotates around x and y, the z axis will rotate, causing the rotation around local z to be different than the rotation around global Z).

I am trying to figure out some way to transform the rotational velocity in the local axes to the rotational velocity in the global axes. This will allow me to integrate the velocites and figure out the global position.

2. Relevant equations

$$\Theta=\int \omega dt$$

$$P_{G}= Rotation Matrix * P_{B}$$

3. The attempt at a solution

So far, I have been trying to use the same rotation matrix that transforms the gyroscope's orientation from the body coordinate frame to the global coordinate frame and attempted to use that to transform the rotational velocity into the global coordinate frame. By recalculating the rotation matrix after each small discrete movement, I thought I would be able to calculate the global angular velocity each time. However, this has resulted in meaningful data. Is this the correct approach and I am just working out the math incorrectly, or is there another approach I should take? Thanks.