Function Repository Resource:

WhewellEquation

Compute the Whewell equation for a plane curve

Contributed by: Jan Mangaldan

ResourceFunction["WhewellEquation"][c,t,{φ,s}]

computes the Whewell equation for tangential angle φ and arc length s of a plane curve c parametrized by t.

Details

The Whewell equation is a natural equation that expresses a curve in terms of its arc length s and tangential angle φ.

Whewell equation for the tractrix:

In[1]:=

$ResourceFunction["WhewellEquation"][ Entity["PlaneCurve", "Tractrix"]["ParametricEquations"][a][t], t, {\[CurlyPhi], s}] // Simplify$

Out[1]=

Whewell equation for the Tschirnhausen cubic:

In[2]:=

$ResourceFunction["WhewellEquation"][ Entity["PlaneCurve", "TschirnhausenCubic"]["ParametricEquations"][ a][t], t, {\[CurlyPhi], s}] // Simplify$

Out[2]=

Citation:
- Yates, R. C. “Intrinsic Equations.” A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards, pp. 123–126, 1952.