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

.. only:: html

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

        Click :ref:`here <sphx_glr_download_matplotlib_plot_complex_pendulumn.py>`
        to download the full example code

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

.. _sphx_glr_matplotlib_plot_complex_pendulumn.py:


Complex contour of a pendulum
=============================

complex surface of a Hamiltoanian 

.. math::

    H(q, p) = \frac{p^2}{2} + k \cos q

with :math:`Re[E]=const.`

.. GENERATED FROM PYTHON SOURCE LINES 16-73



.. image:: /matplotlib/images/sphx_glr_plot_complex_pendulumn_001.png
    :alt: plot complex pendulumn
    :class: sphx-glr-single-img





.. code-block:: default


    import numpy as np
    import matplotlib.pyplot as plt
    from mpl_toolkits.mplot3d import Axes3D

    np.seterr(invalid='ignore')


    twopi = 2*np.pi
    x = np.linspace(-twopi,twopi,100)
    y = np.linspace(-2,2,100)

    x,y = np.meshgrid(x,y)
    eps = 0.5
    Ham = lambda q,p: p**2/2 + eps*np.cos(q)

    #fig, ax = plt.subplots(1,1,projection="3d")
    fig = plt.figure()
    fig.patch.set_visible(0)
    ax = fig.add_subplot(1,1,1,projection="3d")
    ax.patch.set_alpha(0)

    ax.contour(x,y,Ham(x,y),10,zdir='z',offset=0,colors="k")
    E=0
    def P(q,E):
        return np.sqrt(2*(E-eps*np.cos(q)))

    twopi = 2*np.pi
    q = np.linspace(-twopi,twopi,2000) + 0.j
    p = P(q,E)
    ax.plot(q.real, p.real, p.imag, "-r",lw=3)
    ax.plot(q.real, -p.real, p.imag, "-r",lw=3)

    sample=100
    E=0 + np.linspace(0,1,sample)*1.j
    q = np.linspace(-twopi,twopi,sample) + 0.j
    q,E=np.meshgrid(q,E)
    p = P(q,E)
    ax.plot_wireframe(q.real,p.real,p.imag,alpha=0.2)
    ax.plot_wireframe(q.real,-p.real,p.imag,alpha=0.2)
    ax.set_zlim(0,1.5)
    ax.set_xlim(-twopi,twopi)
    ax.set_ylim(-2,2)
    ax.set_xlabel("$\mathrm{Re}(q)$",fontsize=18)
    ax.set_ylabel("$\mathrm{Re}(p)$",fontsize=18)
    ax.set_zlabel("$\mathrm{Im}(p)$",fontsize=18)
    ax.set_xticks([-twopi, -np.pi, 0,np.pi, twopi])
    E=0
    q0=np.arccos(2*E/eps)
    #ax.text(q0,0,0,r"$a$", fontsize=15,bbox=dict(facecolor='w', edgecolor='none', pad=0,alpha=1))
    #ax.text(-q0,0,0,r"$-a$",fontsize=15,bbox=dict(facecolor='w', edgecolor='none', pad=0,alpha=0.8))
    ax.set_yticks([-2,0,2])
    ax.set_zticks([0,1])
    ax.set_xticklabels([r"$-2\pi$", r"$-\pi$", r"$0$", r"$\pi$", r"$2\pi$"])
    #plt.tight_layout()
    #plt.savefig("complex_pen.svg")
    plt.show()


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

   **Total running time of the script:** ( 0 minutes  0.166 seconds)


.. _sphx_glr_download_matplotlib_plot_complex_pendulumn.py:


.. only :: html

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



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

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



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

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


.. only:: html

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

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