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Pedal coordinates are tangential coordinates that describe the position of a point x on a pedal curve γ by two numbers: the distance from the origin r (the pedal point), and the distance from the origin to the tangent of γ at point x. The tangent of the curve depends on the line from the origin to the point.
The pedal equation is defined as 
f(r, p) = 0.
History and Applications of Pedal Coordinates
The name pedal coordinates appears to be due to H.J. Purkiss, a Victorian-era student at the University of Cambridge, who proposed the name because “they are the polar coordinates of the foot of the perpendicular on the tangent” . However, Purkiss didn’t discover the system. According to B. Pourciau  Newton uses pedal coordinates in Principia Mathematica Philosophica Naturalis to show the relationship between the inverse square law and a trajectory; the coordinate system is implied, not explicitly stated . Pedal coordinates are more natural than Cartesian or polar coordinates in some settings, like the study of force problems of classical mechanics in the plane .
Pedal curve image: Sam Derbyshire at English Wikipedia,
 Blaschke, P. PEDAL COORDINATES, DARK KEPLER AND OTHER FORCE PROBLEMS. Retrieved January 16, 2022 from: http://arxiv-export-lb.library.cornell.edu/pdf/1704.00897
 Yates, R. (1974). Curves and Their Properties. The National Council of Teachers of Mathematics.
 The Oxford, Cambridge, and Dublin Messenger of Mathematics, Volume 3. Macmillan and Company, 1866.
 Pourciau, B. Reading the Master: Newton and the Birth of Celestial Mechanics.
 Olivier Bruneau. ICT AND HISTORY OF MATHEMATICS: the case of the pedal curves from
17th-century to 19th-century. 6th European Summer University on the History and Epistemology in Mathematics Education, Jul 2010, Vienna, Austria. pp.363-370. ffhal-01179909f
Stephanie Glen. "Pedal Coordinates" From CalculusHowTo.com: Calculus for the rest of us! https://www.calculushowto.com/pedal-coordinates/
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