What are the Requirements for Deriving Lagrange Equations in Physics?

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I am a physics student in Germany in my second semester!
 
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Hello and :welcome: !
 
I’m a retired ex physicist I guess. Although I have a first degree in theoretical physics and did post graduate studies ( structural phase transitions in strontium Titanate, I did not pursue a career in physics. However it has always been my first love. Since retiring I’ve been interested in quantum computing and quantum mechanics