How do I calculate a corrective torque to remove rotation from my object (except for yaw)?

Questions & Answers
1

I am trying to calculate the torque to apply to an object to correct all rotation, except for the yaw (which is the direction the object is steering in). Here is what I have so far:

 //rotation angle
 float halfAngle = Mathf.Acos(rigidbody.rotation.w);
 float sinHalfAngle = Mathf.Sin(halfAngle);

 //rotation axis
 float x = rigidbody.rotation.x / sinHalfAngle;
 float y = rigidbody.rotation.y / sinHalfAngle;
 float z = rigidbody.rotation.z / sinHalfAngle;    

 Vector3 rotationAxisWithoutYaw = new Vector(x, 0, z);
 float rotationAboutAxisWithoutYaw = ? //this is the critical step

 //unimportant detail below...included so that you can see what I am trying to do
 float desiredRotation = 0;
 float displacementFromDesired = desiredRotation - rotationAboutAxisWithoutYaw;

 float springTorque = -springConstant * displacementFromDesired;
 float inertia = SomeFunctionOf(rigidbody.inertia, rotationAxisWithoutYaw);

 float viscousDampingCoefficient = 2 * Mathf.Sqrt(inertia * springConstant);
 float dampingTorque = -viscousDampingCoefficient * rigidbody.angularVelocity.z;
 float totalTorque = springTorque + dampingTorque;

 rigidbody.AddTorque(rigidbody.transform.forward * totalTorque);

As you can see, I can calculate the axis of rotation to use by ignoring the y-component of the actual rotation vector. But how do I calculate the right angle (without the yaw?) I am unable to visualise it properly, and am totally stuck.

If anyone has any ideas of how to calculate that angle, I would appreciate it!

ht

2

I ended up using calculations based on Euler angles (I normally dread using Euler angles; my experience with such techniques is bad. In this case though, it worked perfectly).

// For rolling
float angularDisplacementZ = rigidbody.rotation.eulerAngles.z;

if(angularDisplacementZ > 180) 
{
    angularDisplacementZ -= 360;
}

float springTorqueZ = -springConstant * angularDisplacementZ ;
float inertiaZ = SomeFunctionOf(rigidbody.inertia, rotationAxisWithoutYaw);

float viscousDampingCoefficient = 2 * Mathf.Sqrt(inertia * springConstant);
float dampingTorqueZ = -viscousDampingCoefficient * rigidbody.angularVelocity.z;
float totalTorqueZ = springTorque + dampingTorque;

rigidbody.AddTorque(rigidbody.transform.forward * totalTorque);

//now do the same for pitching (use X instead of Z)