.TAeZoSysPro.FluidDynamics.Functions.rootsPolyOrder3

Information

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

The discriminant of the second order polynom derives:

• 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;