The equations of the basic spirals are given in polar coordinates. The is the radius and is the angle measured from the positive horizontal axis.The and are constants.
The equation in polar coordinates is the same as the logarithmic spiral but the the constant has a special value
The constant is in units of radians. is the golden number.
The Cornu spiral is also known as the clothoid or Euler’s spiral. The mathematical equation is not as simple as the others shown above. Please refer to the link below.
A spiral that gives the solution to the central orbit problem under a radial force law. Please refer to the link below.