.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/chaos/billiards/plot_bunimovich_stadium.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_chaos_billiards_plot_bunimovich_stadium.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_chaos_billiards_plot_bunimovich_stadium.py:


Bunimovich Stadium (Chaotic)
============================

A billiard particle moves in a straight line at constant speed inside a
closed boundary and undergoes specular reflection,
:math:`\mathbf{v}' = \mathbf{v} - 2(\mathbf{v}\cdot\mathbf{n})\,\mathbf{n}`,
whenever it strikes the boundary. The Bunimovich stadium's boundary is two
straight edges, :math:`y = \pm r` for :math:`|x| \le a`, joined by two
semicircular caps of radius :math:`r` centered at :math:`(\pm a, 0)`, where
:math:`2a` is the straight-edge length. It is chaotic despite having no
concave scatterer: the *focusing* semicircular caps defocus nearby
trajectories after they refocus and diverge past the caps' centers of
curvature (unlike a full circle, whose focusing never gets interrupted by a
flat stretch). This example plots a single trajectory and the resulting
Poincare section.

.. GENERATED FROM PYTHON SOURCE LINES 18-27

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from physicskit.chaos.systems.billiards import BunimovichStadium
    from physicskit.chaos.visualizers.phase_space import plot_billiard_trajectory, plot_poincare_section

    billiard = BunimovichStadium(radius=1.0, straight_length=2.0)








.. GENERATED FROM PYTHON SOURCE LINES 28-30

Trajectory
----------

.. GENERATED FROM PYTHON SOURCE LINES 30-32

.. code-block:: Python

    fig, ax = plot_billiard_trajectory(billiard, pos=billiard.sample_interior_point(), vel=np.array([0.5, 0.9]), n_bounces=100)




.. image-sg:: /api/gallery/chaos/billiards/images/sphx_glr_plot_bunimovich_stadium_001.png
   :alt: BunimovichStadium trajectory
   :srcset: /api/gallery/chaos/billiards/images/sphx_glr_plot_bunimovich_stadium_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 33-37

Poincare section
----------------
As with the Sinai billiard, the section fills in densely rather than
tracing out smooth invariant curves.

.. GENERATED FROM PYTHON SOURCE LINES 37-40

.. code-block:: Python

    fig, ax = plot_poincare_section(billiard, n_rays=40, n_bounces=200)

    plt.show()



.. image-sg:: /api/gallery/chaos/billiards/images/sphx_glr_plot_bunimovich_stadium_002.png
   :alt: BunimovichStadium Poincare section
   :srcset: /api/gallery/chaos/billiards/images/sphx_glr_plot_bunimovich_stadium_002.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.075 seconds)


.. _sphx_glr_download_api_gallery_chaos_billiards_plot_bunimovich_stadium.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_bunimovich_stadium.ipynb <plot_bunimovich_stadium.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_bunimovich_stadium.py <plot_bunimovich_stadium.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_bunimovich_stadium.zip <plot_bunimovich_stadium.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_