Calculating acceleration offset by C.G.

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SUMMARY

This discussion focuses on calculating the acceleration readings of an accelerometer not positioned at the Center of Gravity (C.G.) of an object. The user seeks to determine the accelerometer's output at a specific location (Xa, Za) and how it would differ if placed at the C.G. The conversation references a transformation matrix necessary for this calculation, highlighting the importance of understanding its derivation. The user is advised to consider the context of their question, as it may be more appropriate for a general physics forum.

PREREQUISITES
  • Understanding of accelerometer principles and readings
  • Familiarity with transformation matrices in physics
  • Knowledge of Center of Gravity concepts
  • Basic physics equations related to motion and acceleration
NEXT STEPS
  • Study the derivation of transformation matrices in physics
  • Research the effects of non-C.G. placement on accelerometer readings
  • Explore inertial measurement unit (IMU) applications and calculations
  • Learn about the relationship between acceleration and rotational dynamics
USEFUL FOR

This discussion is beneficial for physics students, engineers working with accelerometers, and anyone involved in the design or analysis of inertial measurement systems.

The Don
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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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