Comparing different methods to solve an Inverted Pendulum problem

A simple reporting tool that shows how you can model an inverted pendulum in a few methods.

In order to solve an inverted pendulum dynamics, you can select several methods:
1. Solving Symbolic equations.
2. Solveing a MATLAB ODE
3. Constructing a Simulink model
4. Designing the system using SimMechanics

This submission show how you can leverage the reporting tools that exist in the MATLAB environemnt in order to compare the solution of all these methods, and show the advantage of each one:
1. Symbolic, complete solution using the Symbolic Math toolbox.
2. Parameter sweep using monte carlo simulation for a MATLAB function.
3. Running the same Simulink dynamic model for different friction values.
4. Modeling the problem and not the equations, using SimMechanics.

In order to run the comparison, simply run the following command:
report symbolic_simmech;

The report template contains examples and how-to do it yourself.

I would like to acknowledge Carlos Osorio, who created some of the files and models in this example.