Calculating acceleration offset by C.G.

[The Don]

Homework Statement

I'm trying to calculate the acceleration an accelerometer would read NOT placed in the Center of Gravity of the object. Let's look at the figure below. The accelerometer was placed in location (Xa,Za) and not in the CG of the object. Given that the accel's output is a_x and a_z at this location (Xa,Za)...what would've the accelerometers have read if placed on the C.G. of object?

Homework Equations

The Attempt at a Solution

Here is an attempt at the solution (http://basicairdata.blogspot.com/2014/05/inertial-measurement-unit-placement.html) however I don't fully understand how they got the transformation matrix.

 

[Isaac0427]

Is this homework? If yes, you probably should not be using the Internet for your attempt. If no, you should put this on the general physics forum.

 

[Isaac0427]

The general physics forum usually gets better answers in my opinion.