Calculating acceleration offset by C.G.

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The discussion focuses on calculating the acceleration readings of an accelerometer not positioned at the Center of Gravity (C.G.) of an object. The user is trying to determine how to adjust the readings from a specific location (Xa, Za) to what they would be at the C.G. The conversation includes a reference to a solution attempt involving a transformation matrix, which the user finds confusing. There is a suggestion that if this is a homework question, the user should refrain from using online resources, while also recommending posting in a general physics forum for potentially better insights. The discussion highlights the complexities of understanding acceleration offsets in relation to an object's C.G.
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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?

upload_2015-12-7_17-31-32.png


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