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Physics
Classical Physics
Mechanics
Conservation law associated with the symmetry of a helix
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[QUOTE="Hiero, post: 6121884, member: 602040"] In a problem in Landau’s mechanics (end of section 9) he asks for the quantity conserved in the field of “an infinite homogenous cylindrical helix.” The solution is that the Lagrangian is unchanged by a rotation of dΦ together with a translation of hdφ/(2π) (about and along the symmetry axis) where h is the pitch of the helix. This implies that M[SUB]z[/SUB]+hP[SUB]z[/SUB]/(2π) is conserved where M and P are the angular and linear momenta and _z means the component along the symmetry axis. It’s a very nice example of Noether’s theorem, but I have one question: Is he silently assuming that the helix is right handed? Surely for a left handed helix the conservation law would be M[SUB]z[/SUB]-hP[SUB]z[/SUB]/(2π), right? Just want to make sure I’m understanding that correctly because Landau never mentions the orientation of the helix, but I think it matters. Thanks. [/QUOTE]
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Conservation law associated with the symmetry of a helix
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