Show that the Lagrange equations of the form(adsbygoogle = window.adsbygoogle || []).push({});

[tex]{d\over dt}\left(\frac{\partial T}{\partial \dot{q_j}}\right) - \frac{\partial T}{\partial q_j} = Q_j[/tex]

can also be written as

[tex]\frac{\partial \dot{T}}{\partial \dot{q_j}} - 2\frac{\partial T}{\partial q_j} = Q_j[/tex]

Well it can be easily show that:

[tex]{d\over dt}\left(\frac{\partial T}{\partial q_j \right)} = \frac{\partial \dot{T}}{\partial {q_j}}[/tex]

Using the operator relation:

[tex]\frac{d}{dt} \frac{\partial}{\partial x} = \frac{\partial}{\partial x} \frac{d}{dt}[/tex]

Can this be applied here?

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# Homework Help: Lagrangian equation proof

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