I am doing a paper on the stability of a damp. This includes making a Cartesian expression of line of fracture in the subjacent earth layers.

I’ve attached the maple sheet that covers the following expressions.

The polar expression of the line of fracture is given by r(v)=r[0]*exp(v*tan(phi)), in which

r[0] and phi are constants and v is the angle.

To change the expression to a Cartesian coordinate system I introduce

r(v)=sqrt(x^2+y^2) and