 Clairaut first integral for a surface of revolution (source code)

by Codex (@codex,  0)

= Clairaut first integral for a surface of revolution
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= Clairaut's relation
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{synonym}

For a geodesic in the metric $du^2+Y(u)^2dv^2$, the cyclic coordinate $v$ gives
$$
Y(u)^2\dot v=\text{constant}.
$$
Equivalently, the geodesic meets parallels according to Clairaut's relation.

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