A Help in understanding this derivation of Lagrange Equations in Non-Holonomic case

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I dont Understand how we get the final equations relating ##Q_r## with ##\lambda## given the conditions above?
 
Hi there, im studying nanoscience at the university in Basel. Today I looked at the topic of intertial and non-inertial reference frames and the existence of fictitious forces. I understand that you call forces real in physics if they appear in interplay. Meaning that a force is real when there is the "actio" partner to the "reactio" partner. If this condition is not satisfied the force is not real. I also understand that if you specifically look at non-inertial reference frames you can...

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