Discussion Forum

I know how to balance fluid-based shear forces around a circle in a 2D stationary study. I set up these variables:

myTheta = atan2((y-mass1.CMY),(x-mass1.CMX))
rotM = intOp((spf.T_stressx*tx+spf.T_stressy*ty)*cRadius)
rotX = -(sin(myTheta)*cRadius*rotFreq)
rotY = (cos(myTheta)*cRadius*rotFreq)

And then solve for the rotFreq (rotational frequency) that sets rotM (rotational moment) to 0, using a global equation.

But what about 3D? The typical way of expressing spherical coordinates involves two planes of rotation, which I will call theta and phi. But, these planes overlap. For example, if we call theta rotation around the Z axis, then theta affects X and Y. If we call phi rotation around the Y axis, then phi affects X and Z. X is in there twice. Maybe this isn’t an issue, but when I’ve set up the equations of motion using:

myTheta = arctan2(Y,X)
myPhi = acos(Z/cRadius)

and then solve for rotational frequencies around theta and phi, I get crazy answers.

I also tried using a 3 rotation system, which essentially involves the same equations as 2D, three times: once for XY, once for XZ, and once for YZ. This seems cleaner to me since you have three axis of rotation and three stress components, allowing you to set up three global equations where setting each stress to 0 solves for the rotational velocity around each axis. But again, I get crazy answers.

I’m not sure that these rotations (in either case) are commutative. If not, that seems like a problem, but not one I know how to address. If that’s not it, then I don’t know what’s going wrong.

Anyone know how to do this?