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;


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!

  • \$\begingroup\$ Will have to take a closer look at this, but one thing I can say is that 'rotationVelocity += addedRotation' almost certainly isn't what you want; you can't simply add Y/P/R values to add rotations, but instead need to properly compose them (via something like quaternion or matrix multiplication). \$\endgroup\$ Sep 11, 2013 at 23:48
  • \$\begingroup\$ Hm, yes. I don't even think what I want is possible with a rotation around a single axis. After yawing and rolling a little bit, I think I basically want one rotation around the up vector (up vector at the time of adding yaw rotation that is - so world y-axis in my example above) and one around the forward axis simultaneously and independently from each other. \$\endgroup\$
    – user31091
    Sep 12, 2013 at 0:21
  • \$\begingroup\$ Note that every rotation can be expressed as a rotation around a single axis (this is actually a fairly deep theorem, and related to quaternion representations) - but that's only true for static rotations, and when you're animating you can certainly expect some 'tumble'. \$\endgroup\$ Sep 12, 2013 at 0:27

1 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.)

  • \$\begingroup\$ I think we're both right - angular velocity is a vector, but the OP's conversion of YPR to an angular velocity vector (and the transformation thereof) still looks awfully suspicious to me. \$\endgroup\$ Sep 12, 2013 at 4:23
  • \$\begingroup\$ Thanks for the response, I will take a closer look a bit later today. I actually do take time into account in my actual code, I'm also aware that angular velocity does not remain constant. I was just simplifying this a lot because I just want to get the actual rotation right. \$\endgroup\$
    – user31091
    Sep 12, 2013 at 11:00

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