Definition:Intrinsic Equation

Definition

Let $C$ be a curve.

An intrinsic equation of $C$ is an equation that defines $C$ using a relation between the intrinsic properties of $C$.

Thus an intrinsic equation defines the shape of $C$ without specifying its position relative to an arbitrarily defined coordinate system.

Whewell Equation

A Whewell equation is an intrinsic equation for a curve $C$ such that $C$ is expressed in terms of its intrinsic properties:

Arc length $s$

Turning angle $\psi$

Also known as

Some sources refer to the general intrinsic equation as a natural equation, but some prefer to reserve this term for the specific example where the intrinsic properties used are curvature and torsion.

Sources

• Weisstein, Eric W. "Natural Equation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NaturalEquation.html