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Rotation of a ball in mid air

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Hi, i’m working for a company where we use gyroscopes to measure the rotation of a ball in 3 dimensions. The output from the sensor is sent 25 times a second and is then converted to deg/s in each of the three axis’s. My task is to analyze the data and then create a program using it. I have some questions regarding this.

1. How do i find a good approximate of the total rotation of the ball in one number. The rotation change (not a lot but it makes things hard) in each of the axis’s while it’s airbourne, but when i use the following formula: sqrt((rotationX)^2 + (rotationY)^2 + (rotationZ)^2) i get almost zero total change of rotation. Is it correct, and why?

2. If i want to measure the total change of rotation between two consecutive samples, is it then correct to use this formula:
sqrt((rotationX.now-rotationX.last)^2 + (rotationY.now-rotationY.last)^2 + (rotationZ.now – rotationZ.last)^2). Why or why not?

Bonus: Does anyone know what or how the gyroscope measures?
Is it torque, just rotation in general or something else?

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