Definition:Turning Angle

Definition

Let $C$ be a curve.

The turning angle $\psi$ of $C$ at a point $P$ is defined by the differential equation:

$\kappa = \dfrac {\d \psi} {\d s}$

where:

$\kappa$ is the curvature at $P$

$\dfrac {\d \psi} {\d s}$ is the derivative of $\psi$ with respect to the arc length $s$.

That is, the turning angle is a measure of how sharply a curve changes direction.

The turning angle is an intrinsic property of $C$.

Also known as

The turning angle is known in some sources as its tangential angle.

Also see

• Definition:Whewell Equation

Sources

• Weisstein, Eric W. "Tangential Angle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TangentialAngle.html