Clairaut's relation
Clairaut's relation, named after Alexis Claude de Clairaut, is a formula in classical differential geometry. The formula relates the distance r from a point on a great circle of the unit sphere to the z-axis, and the angle θ between the tangent vector and the latitudinal circle:
The relation remains valid for a geodesic on an arbitrary surface of revolution.
A formal mathematical statement of Clairaut's relation is:
Pressley explains this theorem as an expression of conservation of angular momentum about the axis of revolution when a particle slides along a geodesic under no forces other than those that keep it on the surface.
