I have moment vector calculated from Force and arm vectors.
import numpy as np
R = np.array([450]).reshape(1,1) # force magnitude
r = np.array([-0.5, 0.5, 0.7071]).reshape(1,3) # force direction unit vector
F = np.dot(R,r) # force vector
u = np.array([-0.15, 0.3, 0.1]).reshape(1,3) # position or arm vector
M = np.cross(u, F) # moment vector
where F and M are array([[-225. , 225. , 318.195]]) & array([[72.9585 , 25.22925, 33.75 ]]) respectively.
How can I back calculate ‘u’ from M and F ?
>Solution :
In most cases, this is not possible as the cross product is not reversible.
This also makes sense if you think about it. Just because you know a force vector and the moment it causes, you can’t possibly know how the body looks like on which the force acts upon.
If you make some constrains on your desired solution (e.g. that u must be orthogonal to M) then you possibly can calculate a solution.
For that you’d have to set up a system of equations with all information you have and try to solve it.