New Hobbyist member seeking help with some math/calculus

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Hello everyone,

I am a 72 year old retired IT worker and I am interested in all things Arduino and a few things PI as hobbies. Although I have completed several dozen Arduino projects and a couple Raspberry PI projects, the latest project has me stumped because the physical motion math of an inverted pendulum is pretty far above my ability to code.

I joined this forum in the hope that someone can help me convert some inverted pendulum motion formulas to C code program language.
 
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Well, an inverted pendulum on Earth is still referential to non-inverted Earth gravity, right? So maybe take the first derivative of position with respect to time (that's velocity); then take the second derivatives with regard to all of the time-dependent vectors, (accelerations), then the 3rd derivative (jerk); then just for fun take the 4th derivative (jounce) and you're good to go -- the inverted pendulum will still be swinging along with velocity,
 
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