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. from: https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.853.7639&rep=rep1&type=pdf
 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