For the interested here is a sketch of the structure.

Direct link to image: http://s1.postimage.org/ddahp3gan/Principle_sketch.png

Original sheet:  BL_-_C.mw

Corrected sheet with regards to Markiyan Hirnyk's comments:  BL_-_C,_corrected.mw

@Axel Vogt 

That is correct. I would like an expression of r(theta)=r0*exp(theta*tan(phi)) in a closed interval in cartisian coordinates. :)

@Axel Vogt 

That is correct. I would like an expression of r(theta)=r0*exp(theta*tan(phi)) in a closed interval in cartisian coordinates. :)

First of all thanks for the detailed description.

I have tried copying your code in a new sheet but the initial solve of L1 with respect to y doesn't work and the plot of "ord" does neither.

You said "It is very doubtful to express y in a closed form as we deal with a transcendental equation." - How about if it is in a closed interval of x? Would you know how to come up with an approximating expression so I get the form of the logerithmical spiral in a limited interval in the cartesian coordinate system that takes the required form of the original equation? - is this what you do with "ord"?

First of all thanks for the detailed description.

I have tried copying your code in a new sheet but the initial solve of L1 with respect to y doesn't work and the plot of "ord" does neither.

You said "It is very doubtful to express y in a closed form as we deal with a transcendental equation." - How about if it is in a closed interval of x? Would you know how to come up with an approximating expression so I get the form of the logerithmical spiral in a limited interval in the cartesian coordinate system that takes the required form of the original equation? - is this what you do with "ord"?

I will appriciate if you would specify: why do you think it is necessary to involve complex numbers?

I certainly would prefer if the final equation can be expressed in a closed interval of x due to I am going to use the expression for physical calculations in a matter length. Both y- and x-coordinates are measured in meters - which gives a mathmatical expression of the spreading of fracture in the soil underneath a dam. Combined within an integration with a piecewise function defining the surface of the earth I wish to find the volume of the exposed soil to be able to evaluate the stability of the structure. Note that the entire structure is evaluated in a plane manner of a cross section.

I will appriciate if you would specify: why do you think it is necessary to involve complex numbers?

I certainly would prefer if the final equation can be expressed in a closed interval of x due to I am going to use the expression for physical calculations in a matter length. Both y- and x-coordinates are measured in meters - which gives a mathmatical expression of the spreading of fracture in the soil underneath a dam. Combined within an integration with a piecewise function defining the surface of the earth I wish to find the volume of the exposed soil to be able to evaluate the stability of the structure. Note that the entire structure is evaluated in a plane manner of a cross section.

I have read the article on the RootOf function. However I do not know how to interpret it in terms of getting a specific equation that I can use to plot y(x).

I can add that x and y of the sought eqaution lies respectively in the interval of 120.6<=x<140,2 and -26.1<=y<05.9. However defining assumptions in solving the equation hasn't gotten me any closer.

Here is the sheet:     Fracture_line_equati.mw

Andreas

I have read the article on the RootOf function. However I do not know how to interpret it in terms of getting a specific equation that I can use to plot y(x).

I can add that x and y of the sought eqaution lies respectively in the interval of 120.6<=x<140,2 and -26.1<=y<05.9. However defining assumptions in solving the equation hasn't gotten me any closer.

Here is the sheet:     Fracture_line_equati.mw

Andreas