How do I convert an inertia tensor from body space to world space?

I've been trying to solve the following problem involving Angular Acceleration and the inertial tensor for about 2 weeks now. I know it's bad ask for a question to be solved, but I'm really at a loss here folks. I'm a high school student who has taken a physics class.

What I'm Trying To Do: I'm trying to give a 3D rigid body an angular acceleration α by applying a torque τ. This is for a program I am writing, so I need to calculate this every time the game updates. I'm working with the Navidia Physx API.

Question: How do I properly convert the inertial tensor, I, from body space to global space?

Starting Variables: desired angular acceleration α(angle axis representation) in global space, the inertia tensor of the object I in body space

What I am trying to find: The torque τ(angle axis representation) in global space that when applied to the body will give it the angular acceleration α.




I've already tried [I_g]=[R]^T[I_b][R] where [R] is the rotation matrix for the rigid body in question, I_g is the inertia tensor in global space, and I_b is the inertia tensor in body space. After I find this I_g , I convert α into Euler Angle representation and multiply it against I_g:
α_x * I_{g xx}
α_y * I_{g yy}
α_z * I_{g zz}

I also have tried keeping I in body space, converting α to body space and using I_m=n^T[I_b]n , where n is the axis of the axis angle representation of α, and I_m is the scalar moment of inertia about that axis. I then take this I_m and multiply it by α in global space.

Both of these calculations have ended up in error. If you would like me to post the code of both of these attempts I am willing to do so, just ask me in the comments.

If you covert between representations ( for example quaternion -> Euler angle), just mention it.

Even though this question is not from Home Work, if you think I should move this question over to HOMEWORK, just comment and I'll do so.

Thank you so much!