Piezoelectric coefficient

Clairaut's relation, named after Alexis Claude de Clairaut, is a formula in classical differential geometry. The formula relates the distance r(t) from a point on a great circle of the unit sphere to the z-axis, and the angle θ(t) between the tangent vector and the latitudinal circle:

$r(t)\cos \theta (t)=\text{constant}.$

The relation remains valid for a geodesic on an arbitrary surface of revolution.

References

• M. do Carmo, Differential Geometry of Curves and Surfaces, page 257.

See also

• Clairaut's theorem

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