Rotations and angular velocity

Question

I'm new to 3D-game programming and I'm having some trouble making objects rotate the way I want them to. I just read Glenn Fiedler's tutorials on game physics, awesome stuff by the way! (http://gafferongames.com/game-physics/physics-in-3d/)

Now, I'm trying to make a simple space sim. If you imagine a spaceship that is not yet rotated in any way (up = Vector3.Up etc..). If I apply some yaw-input (which would increase the angular velocity) I'd then expect the ship to rotate around the up-vector of the ship (which is also the world y-axis at the moment). That works fine. If I would then roll the ship a little bit, I'd expect the ship to roll around its forward axis, but it should also continue to spin around the world y-axis.

At the moment with my implementation instead of keeping it's momentum around the y-axis, it continues to spin around its local up-vector - which is obviously wrong.

I think I understand why this happens with my current implementation, I'm just not sure how to fix it.

This is what I have at the moment, with some minor simplifications (runs every update):

Vector3 addedRotation = new Vector3(pitchInput, yawInput, rollInput);
addedRotation = Vector3.Transform(addedRotation, rotation);
rotationVelocity += addedRotation;

rotation.Normalize();

Quaternion w = new Quaternion(rotationVelocity, 0);
rotation += Quaternion.Multiply(w * rotation, 0.5f);

I'd be very happy if someone could point me in the right direction here. If anything needs clarification, please tell me and I'll try explain it better.

Thanks for taking the time!

Answer 1

rotationVelocity += addedRotation is actually fine. Angular velocity is a vector and adds in the usual way.

The part you may be missing is that in your description of the desired motion, you have a rotation around a constant axis (the global up-vector) combined with a rotation about a rotating axis (the ship's roll axis, which is rotating because of the ship's yaw angular velocity).

This does not correspond to a constant angular velocity, which would be the combination of several rotations about constant axes - e.g. the global up-vector and the ship's roll axis at the moment of adding the roll.

Also note that the quaternion renormalization, rotation.Normalize(), should probably be done after you add 0.5 * w * rotation, not before. (Also, you seem to be missing the delta time, which should be multiplied in there as well - your angular velocities are in radians per frame instead of radians per second.)

(Finally, as a side note I should mention that in general, angular velocity doesn't remain constant over time, even if no torques are acting on an object. Angular momentum remains constant, but for a non-trivial inertia tensor, this results in time-varying angular velocity because the inertia tensor is rotating with the object.)