{% import macros as m with context  %}

.. _pendulum_game:

Week 3: Pendulum with random actions
=============================================================================================================

{{ m.embed_game('week3_pendulum') }}

.. topic:: Controls
    :class: margin

    :kbd:`p`
        Start the simulation
    :kbd:`r`
        Reset the game

    .. rubric:: Run locally

    :gitref:`../irlc/lectures/lec03/lecture_03_pendulum_random.py`


What you see
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The example show the Pendulum example (see (:cite:t:`herlau`, Subsection 10.4.1)). The control signal, :math:`u(t) = 0`, is selected a random in each step.

How it works
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The pendulum is defined as a differential equation given in (:cite:t:`herlau`, Subsection 10.4.1). This differential equation is then simulated using
Runga-Kuttas method (RK4) using the random action signal.