2D CURVES

Version française
See notations below.

Curves beginning by...

 A B C1 C2 D E F G H I JK L M N O P Q R S T U V W X Y Z

CURTATE (CYCLOID, EPICYCLOID, HYPOCYCLOID)

N-SECTRIX

OBLIQUE (CISSOID  OR STROPHOID/)

PROLATE (TROCHOID, EPITROCHOID, HYPOTROCHOID)

RIGHT CISSOID,  STROPHOID

SLUZE'S CUBIC

NOTATIONS

: curve being studied.
M : running point of the curve .
(D) : straight line, (C) : circle.
( O) :  direct orthonormal frame, of axes Ox and Oy.
( x, y): Cartesian coordinates of M.
X and Y : projected points from M on Ox and Oy.
: affix of M.
: polar coordinates of M .
t : parameter (= time).
speed vector.
acceleration vector.
: tangent.
: normal.
s : curvilinear abscissa.
,)
: tangent vector.
: measure of the Cartesian tangential angle , defined by , i.e. , therefore  .

: Measure of the polar tangential angle , defined by, therefore  ; moreother .

angle of contingence.

: normal vector.
 Coordinates of in the basis in the basis

V : algebraic speed (  ).

AT : tangential acceleration, AN : normal acceleration (  ).

 H : projected point from O on the tangent to the curve. :  pedal radius ( ). : radius of curvature (,). : curvature. : centre of curvature in M. Cartesian equation, parametrization : characterization in x and y. Polar equation, parametrization : characterization in r and q. Bipolar equation : characterization in r = FM and r' = FM (F and F' are the poles). Intrinsic equation 1 (or intrinsic equation of Cesaro): characterization in RC and s; one integrates it by using :  allowing to obtain the Intrinsic equation 2 (or intrinsic equation of Whewell) : characterization in s and j ; one integrates it by using : .

 T: intersection point of the tangent with the Ox axis and also value of = "tangent". = "sub tangent". N: Intersection point of the normal with the Ox axis and also value of  = "normal". = "sub normal". : Intersection point of the tangent with the perpendicular at O to (OM) and also value of  = "polar tangent". = "sub polar tangente". NP: Intersection point of the normal with the perpendicular at O to (OM) and also value of  = " polar normal". = " sub polar normal".