Modelica.Math.Nonlinear.Examples

Examples demonstrating the usage of the functions in package Nonlinear

Information

Extends from Modelica.Icons.ExamplesPackage (Icon for packages containing runnable examples).

Package Content

Name	Description
quadratureLobatto1	Integrate integral with fixed inputs
quadratureLobatto2	Integrate integral with user dependent inputs
solveNonlinearEquations1	Solve nonlinear equations with fixed inputs
solveNonlinearEquations2	Solve nonlinear equations with user dependent inputs
QuadratureLobatto3	Integrate function in a model
UtilityFunctions	Utility functions that are used as function arguments to the examples

Modelica.Math.Nonlinear.Examples.quadratureLobatto1

Integrate integral with fixed inputs

Information

This example integrates the following integrands with function quadratureLobatto and compares the result with an analytical solution. The examples also demonstrate how additional input arguments to the integrand function can be passed as additional arguments. The following integrals are computed:

• integral(sin(x)*dx) from x=0 to x=1
• integral(sin(5*x)*dx) from x=0 to x=13
• elliptic integral from x=0 to pi/2

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Modelica.Math.Nonlinear.Examples.quadratureLobatto2

Integrate integral with user dependent inputs

Information

This example solves the following integrands with function quadratureLobatto. The user can set the parameters, like "w" or "k", and can experiment with different integration intervals. The following integrals are computed:

• integral(sin(x)*dx)
• integral(sin(w*x)*dx)
• elliptic integral

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Modelica.Math.Nonlinear.Examples.solveNonlinearEquations1

Solve nonlinear equations with fixed inputs

Information

This example solves the following nonlinear equations with function solveOneNonlinearEquation and compares the result with the available analytical solution. The examples also demonstrate how additional input arguments to the nonlinear equation function can be passes as additional arguments. The following nonlinear equations are solved:

• 0 = u^2 - 1
• 0 = 3*u - sin(3*u) - 1
• 0 = 5 + log(u) - u

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Modelica.Math.Nonlinear.Examples.solveNonlinearEquations2

Solve nonlinear equations with user dependent inputs

Information

This example solves the following nonlinear equations with function solveOneNonlinearEquation. The user can set the parameters, like "w" or "m", and can experiment with different start intervals. The following nonlinear equations are solved:

• 0 = u^2 - 1
• 0 = 3*u - sin(w*u) - 1
• 0 = p[1] + log(p[2]*u) - m*u

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Modelica.Math.Nonlinear.Examples.QuadratureLobatto3

Integrate function in a model

Information

Technically, this example demonstrates how to utilize a function as input argument to a function in a model.

From a modeling point of view, the example demonstrates in very simplified way the basic approach to model distributed systems with the Ritz method. The displacement field u(c,t) of a particle (where c is the undeformed position and t is time) is hereby approximated by space-dependent mode shapes Φ(c) and time-dependent modal amplitudes q(t), that is u = Φ(c)*q(t). When inserting this decomposition in the equations of motion and then integrating over all particles, terms such as ∫(Φ(c) dc)*q(t) appear, where the time-invariant integral term can be computed beforehand once with the Lobatto method. By this approach the partial differential equations are transformed to a system of ordinary differential equations.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Parameters