I don't know what I am doing wrong, but hell if I can figure it out.

position vector "R" going from point A to point B

3 forces act on point B, one on each axes (each direction is a different magnitude) and yeilds the force vector F

3 moments act on the body on each axes yeilding the moment vector M

R=<x, y, z>
F=<Fx, Fy, Fz>
M=<Mx, My, Mz>

Point A has zero moment in any direction. I know all of the forces and the moments at point B and need to find the position vector relating A and B.


So . . .
Ma = 0 = M + R x F
-M = R x F
<-Mx, -My, - Mz> = <y(Fz) - z(Fy), z(Fx) - x(Fz), x(Fy) - z(Fx)>

then break it down into the i, j, and k compontents and get the following three equations

y(Fz) - z(Fy) = -Mx
z(Fx) - x(Fz) = -My
x(Fy) - y(Fx) = -Mz


I know this should be simple, but I can't seem to solve for x,y,z. I should be able to solve the second and third eqns for z and y, respectively, and substitute that into the first equation for an equation in terms of just x. But everytime I do, the x's cancel out. I tried gaussian elimination, but somewthing went wrong with that too.

Where am I going wrong

[Edited on August 28, 2006 at 7:34 PM. Reason : ]

8/28/2006 7:30:30 PM

do you have a picture

8/28/2006 8:50:07 PM

here is an example



You have a position vector and a Force Vector.

The moment vector M = A X Fa

So just doing the cross product, you can easily find that
M=16i - 8j - 8k



Now suppose you are given the moment vector M, and the force vector Fa, and need to find the position vector R. That is what I am trying to do.

[Edited on August 28, 2006 at 9:39 PM. Reason : ]

8/28/2006 9:11:49 PM

is this a problem in a book?

8/28/2006 9:27:20 PM

No

What my real situation is is that I have experimental data from wind tunnel tests. A load cell determined Fx, Fy, Fz, Mx, My, and Mz for each different test. These forces and moments act around the center of gravity (CG) of the body. I am trying to find where the center of pressure (COP) is in relation to the CG. At the COP, the sum of hte moments is 0.


[Edited on August 28, 2006 at 9:40 PM. Reason : ]

8/28/2006 9:34:44 PM

no one remembers doing moments from 3d forces?

8/29/2006 9:15:52 AM

ah . . . apparently the problem is that there is more than one unique solution

8/29/2006 5:12:09 PM