Question

what is pedal equation

Answer 1

For a plane curve C and a given fixed point O, the pedal equation of the curve is a relation between r and p where r is the distance from O to a point on C and p is the perpendicular distance from O to the tangent line to C at the point.

Answer 2

PEDAL EQUATION


For a plane curve C and a given fixed point O, the pedal equation of the curve is a relation between r and p where r is the distance fromO to a point on C and p is the perpendicular distance from O to the tangent line to C at the point. The point O is called the pedal point and the values r and p are sometimes called thepedal coordinates of a point relative to the curve and the pedal point. It is also useful to measure the distance of O to the normal {\displaystyle p_{c}}(the contrapedal coordinate) even though it is not an independent quantity and it relates to {\displaystyle (r,p)} as {\displaystyle p_{c}:={\sqrt {r^{2}-p^{2}}}}.

Some curves have particularly simple pedal equations and knowing the pedal equation of a curve may simplify the calculation of certain of its properties such as curvature. This coordinates are also well suited for solving certain type of force problems in classical mechanics and celestial mechanics.