The library you are using to integrate the tensor may also provide you some function to calculate its moment around some given point.

It does -- see Re^3: [OT] Forces. -- but at this point I am unsure how to make use of it?

All I know about the value returned is this quote (the only one) from the manual:

Rˆ2 (i.e. Moment of Inertia/density) This integral is used to determine the moment of inertial of the selected blocks. To obtain moment of inertia, the result of this integral must be multiplied by the density of the selected region. For 2D planar problems, the moment of inertia about the z-axis (i.e. about x=0,y=0)

In terms of my diagram, x=0, y=0 is the point B.

The moment of inertia is a different thing (which BTW, you also need to know).

I was actually referring to the moment of the force or the torque, which given your tensor field F(v) with v the vector (x, y, 0), it is the integral of the torque field defined as the vectorial product F(v) ^ v (supposing, the rotational axis is (0, 0, z)).

In the same way for linear movement you have the equation F = m * a, for a rotational movement there is T = I * alfa where T is the torque or moment of force, I the moment of inertia, and alfa the angular acceleration.

In the same way for linear movement you have the equation F = m * a, for a rotational movement there is T = I * alfa where T is the torque or moment of force, I the moment of inertia, and alfa the angular acceleration.

Problem. This is a static 2D FEA. Literally, a moment in time; so no time delta, no acceleration, no motion. And so, no direct means to determine any of them from the model.

My task is to try and turn that into a dynamic simulation. Literally, a time-lapse movie.

Start from the known starting point, run the model, extract an image of the resultant tensor field and save.

Then, try to approximate how the model must change in order to simulate the passing of a short elapsed time, and adjust the model to suit, then repeat. With small enough steps and enough iterations, a reasonable facsimile of the dynamics of the mechanism should be inferable. But the "approximation" can only be just that, because the model does not do dynamic.

The body in the problem is effectively a collection of varyingly magnetic materials. The forces involved are multiple magnetic fields impinging from essentially all directions. As the body moves relative to the magnetic field sources, the effects of those fields vary constantly; (with the square of the distance between the components of the body and the field sources impinging on them).

This problem is directly analogous to the N-body problem. Whilst it is possible to approximate a solution, calculating an exact solution would require huge resources of both time and processor power. Perhaps possible for the likes of NASA, Lawrence Livermore National Laboratory, and similar bodies, but certainly not for the likes of me :)

So, I'm back to needing to use intuition and fudge factoring to attempt to approximate the solution.

To my advantage, I do have some information not presented in the problem description -- because it arises from things outside of that description -- that tell me that the body will precess by a fixed and calculable number of degrees around A for every full revolution of the combined body/link assembly around B. Think of the 26,000 year cycle of the precession of Earth's poles as it revolves around the Sun.

In the example described and from which the numbers I've been quoting derive; that is (conveniently) 90° of body-around-A precession for every 360° of rotation of the assembly around B. This is easily incorporated into the calculations as a fudge factor.

Which brings me back to the OP description and my assumption that (in the small, and in isolation of the causes of the precession described above), the orientation of the body with respect to B will remain constant as point A rotates around B. Hence, my conclusion that the body will counter-rotate with respect to A as A revolves around B.

And so I come back to trying to work out how much counter rotation around A is required for each degree of A's rotation around B in order to maintain the body's orientation with respect to B?

As you can see from my diagram -- albeit that the angles are exaggerated -- the amount of the counter-rotation is not the same as that of the force vector. My conclusion is that it is (approximately) equal to the rotation of A about B. And that is determined by the angle at which the force vector's influence on the position of F (or equivalently A) comes to a halt because the force has moved the point F (and thus A) such that they form a straight line with B.

And that's what I am seeking either: a) confirmation of; or b) a cogent refutation of.

Thoughts? :)

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