[JamesTerm]

Originally Posted by Ether

omega = ((sFR*cos(atan2(W,L)+pi/2-aFR)+sFL*cos(atan2(-W,L)+pi/2-aFL)
+sRL*cos(atan2(-W,-L)+pi/2-aRL)+sRR*cos(atan2(W,-L)+pi/2-aRR))/4)/
(sqrt(L^2+W^2)/2);

This is what I have confirmed the omega equation to be:

const double omega = (((_.sFR*cos(atan2(W,L)+(HP-_.aFR))/4)+
(_.sFL*cos(atan2(-W,L)+(HP-_.aFL))/4)+
(_.sRL*cos(atan2(-W,-L)+(HP-_.aRL))/4)+
(_.sRR*cos(atan2(W,-L)+(HP-_.aRR))/4)));

Since it is just about Christmas I'll show you a similar equation I wrote (that helped me figure this one out)... This is what I use when appling a vectored force to a point within a rigid body.

void PhysicsEntity_2D::ApplyFractionalForce( const osg::Vec2d &force, const osg::Vec2d &point,double FrameDuration )
{
	//Use this as a "get by" if the code doesn't work properly
#if 0
	ApplyFractionalForce(force,FrameDuration);
	return;
#endif
	//Here is a rough draft to solve in 2 dimensions
	//A=atan2(py,px)   point
	//M=pi/2 - A
	//L=atan2(fy,fx)  force
	//N=L+M
	//Y=sin(N)*f.length = contribution for force
	//X=cos(N)*f.length = contribution for torque

	double TorqueToApply;
	osg::Vec2d ForceToApply;
	double RadialArmDistance;

	{
		double A=atan2(point[1],point[0]);
		double M=(M_PI/2) - A;
		double L=atan2(-force[1],-force[0]);
		double N=L+M;

		double ForceLength= sqrt((force[1]*force[1])+(force[0]*force[0]));
		RadialArmDistance= sqrt((point[1]*point[1])+(point[0]*point[0]));
		//I've reserved a special case for ships which haven't specified  their radius size, in which case we simply factor out the radial arm too
		if ((m_RadiusOfConcentratedMass==1.0)&&(RadialArmDistance>1.0)) RadialArmDistance=1.0;

		//Fr = t   ... We should multiply force by the radial arm distance to get the torque
		//but instead,  we pass it off to physics where the multiply gets applied directly against the Radius of Concentrated Mass
		//We could multiply here but doing it the other way keeps the torque value low, which also makes it easier to debug
		TorqueToApply=(cos(N)*ForceLength); 
	}

	osg::Vec2d vecToCenter = -point;
	//Note we should be able to support a point set at 0,0,0 in which case we use the force itself as the direction... otherwise a zero'd point
	//results in a zero'd vector which would omit applying the force
	if (vecToCenter.length2()==0.0)
		vecToCenter=-force;

	vecToCenter.normalize();

	ForceToApply = vecToCenter * (force * vecToCenter);

	ApplyFractionalForce(ForceToApply,FrameDuration);
	ApplyFractionalTorque(TorqueToApply,FrameDuration,RadialArmDistance);
}