Determine rotation matrix given angular velocity tensor and time

[Cade]

Homework Statement

I'm given an angular velocity tensor as shown.

From this, I can extract the angular velocity. As I understand it, the angular velocity tensor matrix is the derivative of the rotation matrix. I have to determine the rotation matrix after t seconds.

Homework Equations

The Attempt at a Solution

From this, I could extract the angular velocity, convert it to a quaternion, multiply it by t and then convert it to a rotation matrix, but I'm not sure if this is the way to go.

 

[anathema]

Hello,

Your approach to extract the angular velocity and convert it to a quaternion is correct. However, instead of multiplying it by t, you can directly use the angular velocity tensor matrix to determine the rotation matrix after t seconds. The angular velocity tensor matrix is a representation of the time derivative of the rotation matrix, so using it to determine the rotation matrix after t seconds is a valid approach.

To do this, you can use the formula:

R(t) = exp(W*t) * R(0)

where R(t) is the rotation matrix after t seconds, W is the angular velocity tensor matrix, and R(0) is the initial rotation matrix.

I hope this helps. Good luck with your problem!