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DO NOT USE THIS TAG just because the question contains an equation of motion!
1
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Showing the invariance of the equations of motion
It is strange to me that for a symmetry which involves $\dot{x}$, there seems to always appear a term with $\dddot{x}$ in the variation of the equations of motion, which doesn't makes much sense. I th …
3
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Is it valid to replace the equations of motion inside a symmetry?
For example, this symmetry:
$$\delta q^{i}=\epsilon(q^{i}-2\dot{q}^{i}t)$$
it's derivative is:
$$\delta\dot{q}^{i}=-\epsilon(\dot{q}^i +2\ddot{q}^i t)$$
There appears $\ddot{q}^{i}$ in this expres …