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Chord of Curvature, Math, Marketing Management
Definition: If C be the circle of curvature at any point P on a curve, then a chord of C through P in a given direction is called the chord of curvature in that direction.
The Lengths of Chords of Curvature
Case I: Let y = ƒ(x) be any cartesian curve. Draw the circle of curvature at any point P on the curve. Let the tangent at P make and angle ? with the xaxis. Let PQ and PS be the chords of curvature parallel to xaxis and yaxis respectively. Complete the rectangle PQRS. We have PR = 2?. Now,
PQ = 2? cos (90  ?) = 2? sin ?,
And PS = 2? cos ?.
Hence
The chord of curvature parallel to the xaxis = 2? sin ?,
The chord of curvature parallel to the yaxis = 2? cos ?.
Posted Date: 1/31/2012 10:55:35 PM  Location : United States
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