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 Quote by FeX32 The Lagrangian can be expressed about any coordinate that can be written in the form: \frac{d}{dt}\left(\frac{∂L}{∂\dot{q}_i}\right)-\frac{∂L}{∂q_i}=Q_i Where $L$ is the Lagrangian (kinetic energy - potential energy)
I may be being blindingly stupid here, but I don't see how that answers my original question. What is it about the position and velocity components of a free particle which means they cannot fit that equation?