Differences between the variations in Noether's theorem and Hamilton's Principle

Asked Mar 29 '20 at 20:36

Active Mar 29 '20 at 21:25

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Noether’s theorem can be defined for the invariance of the action under variations of paths induced by a coordinate transformation which depends continuously on a parameter, $\epsilon$, $q_i(t) \rightarrow \bar{q}_i(t, ε)$, $\bar{q}_i(t, 0) = q_i(t)$.

What differences are there between the variations, $δ_{q_i}$, considered in Hamilton’s principle, and the variations considered in Noether’s theorem?

edited Mar 29 '20 at 21:25

Qmechanic

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asked Mar 29 '20 at 20:36

I don't think there is a difference, since both variations can be thought of as a bunch of virtual displacements. – Thermodynamix Mar 29 '20 at 20:41
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In Hamilton's principle, the variation of the trajectory must vanish at the initial and final point. – Tomáš Brauner Mar 29 '20 at 21:00
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Possible duplicate: https://physics.stackexchange.com/q/299111/2451 – Qmechanic Mar 29 '20 at 21:23

Differences between the variations in Noether's theorem and Hamilton's Principle

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