.TAeZoSysPro.FluidDynamics.Functions.rootsPolyOrder3

Find the roots of a 3 order polynome of kind ax3 + bx2 + cx + d = 0

Information

rootsPolyOrder3

This function computes the vector of roots, roots=(x1, x2, x3}, of third order polynom P(x):

The process to get the roots derives from CARDAN's method available at the following link.
To sum up:

The following change of variable is performed to derive to:

if the determinant Δ of the 3rd order polynom is strictly positif (Δ > 0), the roots derive:

if Δ = 0, the roots derive:

if Δ > 0, the only real root derives:

If 'a' is bellow 1e-10, the polynom is assumed to be 2nd order

The discriminant of the second order polynom derives:

If Δ < 0, there are no real root and an error message is raised.
If Δ = 0, there is one double solution:

If Δ > 0, the two real roots derives.

If 'a' and 'b' are bellow 1e-10, the polynom is assumed to be 1st order

The first root derives:

In case where a roots has no assigned value, its default value is 0.

Interface

function rootsPolyOrder3
  extends Modelica.Icons.Function;
  input Real a "Polynom coefficients";
  input Real b "Polynom coefficients";
  input Real c "Polynom coefficients";
  input Real d "Polynom coefficients";
  output Real roots[3];
end rootsPolyOrder3;

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