When deriving the conserved quantity in the case of space-time symmetry, a line in my notes goes from:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\int{dt.(1+\epsilon\dot{\xi}).L[q(t+\epsilon\xi)+{\delta}q(t+\epsilon\xi)]} - \int{dt.L[q(t)+{\delta}q(t)]}[/tex]

where L is the Lagrangian and [tex]\xi[/tex] is a function of time and both integrals are over the same time interval, to:

[tex]\int{\dot{\xi}L+\xi\frac{dL}{dt}+O(\epsilon^{2})}[/tex]

I can't see how these two lines equal one another.

How does the [tex]O(\epsilon^{2})[/tex] come about?

Thanks.

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# Space-time symmetry (Langrangian Mechanics)

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