################################
Describing equations in Modelica
################################

In this session, you'll learn how to use the OpenModelica environment
to simulation differential equations written in a Modelica ``model``.

First, if you want OpenModelica installed on your own computer,
see :ref:`OM-install`.

Main ressources needed:

* Michael Tiller's online book *"Modelica by Example"* [Tiller-2014]_

    * first chapter `Basic Equations`_ of the first part "Describing Behavior" 

* OpenModelica User’s Guide [OM-guide]_

    *  `OMEdit introduction`_ section

ODE: Vehicle suspension
=======================

Your boss want you to quickly check that the spec for the damping
factor α is appropriate (i.e. that the chassis doesn't oscillate too much).
Model for the suspension (agregated for all wheels) is given on :numref:`suspension`.

Objective: Write and simulate a Modelica model to check the behavior of the chassis.

To start with, let's consider that the wheel stays always in contact with the road.

.. figure:: ./diagrams/suspension.png
    :width: 25 em
    :name: suspension

    diagram of a 1D model for a vehicle suspension

parameters:

======   =================  ================
mass m   spring constant k  damping factor α
======   =================  ================
10³ kg   30.10³ N/m         2.10³ N/(m/s)
======   =================  ================


.. admonition:: Useful tip for OpenModelica
    :class: attention
    
    Observe that the value of model parameters can be changed at simulation time,
    without recompiling the model. This saves the recompilation time.
    In the Plotting interface use the "Re-simulate" button.

What's next
===========

Possible next activities:

* Uncovering the mysteries of OpenModelica: :ref:`OM-simflow`
* More advanced equations: :ref:`discrete-eq`
* Start using physical components: :ref:`use-comp`


.. _Basic Equations: https://mbe.modelica.university/behavior/equations/
.. _OMEdit introduction: https://openmodelica.org/doc/OpenModelicaUsersGuide/latest/omedit.html