= Helical symmetry
{title2=$(\theta,z)\mapsto(\theta+\epsilon,z+b\epsilon)$}
A <helical symmetry> combines an axial <rotation> and a proportional axial <translation>. A <helix> with $z=b\theta$ is unchanged as a set by this transformation. If a mechanical <Lagrangian> is invariant, the <Noether conserved quantity for a mechanical point symmetry> is $L_z+bP_z$, where the two momenta include all moving components. Pure axial <rotation> and pure axial <translation> need not separately be <symmetries>. The <helical symmetry of a potential> is a related special case in which the constraint is replaced by an invariant potential.<Classical Dynamics by David Tong>[online chapter 2, §2.4.1, conserved momentum for a continuous coordinate transformation]{ref}
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