Natural Parametric Equations

The natural parametric equations of a curve are parametric equations that represent the curve in terms of a coordinate-independent parameter, generally arc length s, instead of an arbitrary variable like t.

For example, while the usual parametric equations for circle of radius a centered at the origin are given by

x(t) = acost

(1)

y(t) = asint,

(2)

since the arc length function is given by

s(t)=at,

(3)

the natural parametric equations are

x(s) = [画像:acos(s/a)]

(4)

y(s) = [画像:asin(s/a).]

(5)

See also

Natural Equation, Parametric Equations

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Cite this as:

Weisstein, Eric W. "Natural Parametric Equations." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NaturalParametricEquations.html

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