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STEVAL-EDUKIT01 inverted pendulum equations

FIann.2
Associate II

I came across the STEVAL-EDUKIT01 system and I'm trying to follow the manual downloadable from the ST website but I already have difficulty understanding the equations that govern the inverse pendulum presented in appendix D on page 143 of this manual(https://drive.google.com/file/d/1TShSZnhovXGBWyp9U5gxpYn494UExrGA/view).

In particular I do not understand the formula dR = r sin𝜙 cos𝜙 - l / 2 sin𝜃, because from the equations that I am able to write it results instead dR = rsin𝜙 − l / 2sin𝜃

so I don't understand where the term sin𝜙 cos𝜙 comes from.

In fact, continuing a simplification is then made for small angles so that I get the same result as dR = r 𝜙 - l / 2 𝜃.

I do not understand the simplifications on page 145 as I do not understand the term

(2/3 + Irotor) but (7/6 + Irotor).

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