plane curve curvature
quantifies the degree of local curvature of the parameter curve.
symbols, variables and units
x,y: coordinates (m); apostrophe: derivation of the same parameter; κ: curvature (m⁻¹).
applicable conditions and boundaries
curve is quadratically differentiable and the velocity vector is non-zero. The
formula source code
The following is a copyable LaTeX expression.
\kappa=\frac{\lvert x'y''-y'x''\rvert}{(x'^2+y'^2)^{3/2}}Reference and Extended Learning
OpenStax · Calculus Volume 3 ↗is organized according to model definition and assumptions. Please check actual conditions and original literature before engineering, research and clinical use.
curvaturecurve
The