AlephClo
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How to derive Nielsen equation from Lagrange equation
How to derive Nielsen equation from Lagrange equation?
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AlephClo
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I have done couple hours of research and tried to derive it myself. The best that I found is this, but I do not understand where the commutator come from. It does not seem to be the Poisson braket commutator applied to T either (A,B) = AB-BA . Nor that I understand where the (2) relationship comes from. Thank you
![Printed equations from a text on Lagrangian mechanics: total time derivative d/dt expansion, commutator identity [∂/∂q̇^j, d/dt] = ∂/∂q^j, the identity for d/dt ∂T/∂q̇^j, and the Lagrange equations Q_j = d/dt ∂T/∂q̇^j − ∂T/∂q^j − 2∂T/∂q^j.](https://www.physicsforums.com/attachments/upload_2019-1-9_5-4-47-png.237044/ "upload_2019-1-9_5-4-47.png")
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![Printed equations from a text on Lagrangian mechanics: total time derivative d/dt expansion, commutator identity [∂/∂q̇^j, d/dt] = ∂/∂q^j, the identity for d/dt ∂T/∂q̇^j, and the Lagrange equations Q_j = d/dt ∂T/∂q̇^j − ∂T/∂q^j − 2∂T/∂q^j.](/data/attachments/220/220125-0eea2e87f0d1857e238d54617f438bc2.jpg?hash=Duouh_DRhX)
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Except where it says ##=0## one should read ## = Q_j##
AlephClo
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Thank you BvU.