Intrinsic coordinates

Intrinsic coordinates is a coordinate system which defines points upon a curve partly by the nature of the tangents to the curve at that point. A point is given as (s, Ψ) where s is the length of the curve from a set point (often the origin, in the case of the diagram on the right, point A) and Ψ is the angle which the tangent to the curve at that point makes with the origin.

Related Topics:
Coordinate system - Curve - Tangent

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This coordinate system has limited use, it may break down entirely when straight lines are considered, but inspection reveals three interesting properties regarding the rate of change of its variables, namely:

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:rac{dy}{dx} = an Psi

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:rac{dx}{ds} = cos Psi

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:rac{dy}{ds} = sin Psi

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