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

.. only:: html

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

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

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

.. _sphx_glr__gallery_CatenaryCase_run_catenary.py:


Catenary
========

This case simulates a rod hanging under its own weight, forming a catenary
curve. The rod is fixed at both ends and is allowed to settle into its
equilibrium position.

.. GENERATED FROM PYTHON SOURCE LINES 9-20

.. code-block:: Python


    from collections import defaultdict
    import numpy as np

    import elastica as ea

    from post_processing import (
        plot_video,
        plot_catenary,
    )








.. GENERATED FROM PYTHON SOURCE LINES 21-24

Simulation Setup
----------------
We define a simulator class that inherits from the necessary mixins.

.. GENERATED FROM PYTHON SOURCE LINES 24-35

.. code-block:: Python



    class CatenarySimulator(
        ea.BaseSystemCollection, ea.Constraints, ea.Forcing, ea.Damping, ea.CallBacks
    ):
        pass


    catenary_sim = CatenarySimulator()
    final_time = 30








.. GENERATED FROM PYTHON SOURCE LINES 36-39

Rod Setup
---------
We set up the rod parameters. This rod is affected by a gravity force.

.. GENERATED FROM PYTHON SOURCE LINES 39-81

.. code-block:: Python


    n_elem = 500
    time_step = 1e-4
    total_steps = int(final_time / time_step)
    rendering_fps = 20
    step_skip = int(1.0 / (rendering_fps * time_step))

    start = np.zeros((3,))
    direction = np.array([1.0, 0.0, 0.0])
    normal = np.array([0.0, 0.0, 1.0])
    binormal = np.cross(direction, normal)

    # catenary parameters
    base_length = 1.0
    base_radius = 0.01
    base_area = np.pi * (base_radius**2)
    volume = base_area * base_length
    mass = 0.2
    density = mass / volume
    E = 1e4
    poisson_ratio = 0.5
    shear_modulus = E / (poisson_ratio + 1.0)

    base_rod = ea.CosseratRod.straight_rod(
        n_elem,
        start,
        direction,
        normal,
        base_length,
        base_radius,
        density,
        youngs_modulus=E,
        shear_modulus=shear_modulus,
    )

    catenary_sim.append(base_rod)

    # Add gravity
    catenary_sim.add_forcing_to(base_rod).using(
        ea.GravityForces, acc_gravity=-9.80665 * normal
    )








.. GENERATED FROM PYTHON SOURCE LINES 82-83

Damping is added to the system to help it reach a steady state.

.. GENERATED FROM PYTHON SOURCE LINES 83-92

.. code-block:: Python


    # add damping
    damping_constant = 0.3
    catenary_sim.dampen(base_rod).using(
        ea.AnalyticalLinearDamper,
        damping_constant=damping_constant,
        time_step=time_step,
    )








.. GENERATED FROM PYTHON SOURCE LINES 93-96

Boundary Conditions
-------------------
We fix both ends of the rod using the `FixedConstraint`.

.. GENERATED FROM PYTHON SOURCE LINES 96-104

.. code-block:: Python


    # fix catenary ends
    catenary_sim.constrain(base_rod).using(
        ea.FixedConstraint,
        constrained_position_idx=(0, -1),
        constrained_director_idx=(0, -1),
    )








.. GENERATED FROM PYTHON SOURCE LINES 105-108

Callback
--------
We define a callback class to record the rod state during the simulation.

.. GENERATED FROM PYTHON SOURCE LINES 108-141

.. code-block:: Python



    # Add call backs
    class CatenaryCallBack(ea.CallBackBaseClass):
        """
        Call back function for continuum snake
        """

        def __init__(self, step_skip: int, callback_params: dict) -> None:
            super().__init__()
            self.every = step_skip
            self.callback_params = callback_params

        def make_callback(
            self, system: ea.typing.RodType, time: np.float64, current_step: int
        ) -> None:

            if current_step % self.every == 0:

                self.callback_params["time"].append(time)
                self.callback_params["step"].append(current_step)
                self.callback_params["position"].append(system.position_collection.copy())
                self.callback_params["radius"].append(system.radius.copy())
                self.callback_params["internal_force"].append(system.internal_forces.copy())

                return


    recorded_history: dict[str, list] = defaultdict(list)
    catenary_sim.collect_diagnostics(base_rod).using(
        CatenaryCallBack, step_skip=step_skip, callback_params=recorded_history
    )








.. GENERATED FROM PYTHON SOURCE LINES 142-145

Finalize and Run
----------------
We finalize the simulator, create the time-stepper, and run.

.. GENERATED FROM PYTHON SOURCE LINES 145-156

.. code-block:: Python


    catenary_sim.finalize()
    timestepper: ea.typing.StepperProtocol = ea.PositionVerlet()

    dt = final_time / total_steps
    time = 0.0
    for i in range(total_steps):
        time = timestepper.step(catenary_sim, time, dt)
    position = np.array(recorded_history["position"])
    b = np.min(position[-1][2])








.. GENERATED FROM PYTHON SOURCE LINES 157-161

Post-processing
---------------
Finally, we can save a video of the simulation and plot the final
shape of the catenary.

.. GENERATED FROM PYTHON SOURCE LINES 161-172

.. code-block:: Python


    # plotting the videos
    filename_video = "catenary.mp4"
    plot_video(
        recorded_history,
        video_name=filename_video,
        fps=rendering_fps,
        xlim=[0, base_length],
        ylim=[-0.5 * base_length, 0.5 * base_length],
    )





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    plot video

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.. GENERATED FROM PYTHON SOURCE LINES 173-178

.. video:: ../../../examples/CatenaryCase/catenary.mp4
   :width: 720
   :autoplay:
   :muted:
   :loop:

.. GENERATED FROM PYTHON SOURCE LINES 180-181

plotting the catenary positions after simulation.

.. GENERATED FROM PYTHON SOURCE LINES 181-186

.. code-block:: Python

    plot_catenary(
        recorded_history,
        xlim=(0, base_length),
        ylim=(b, 0.0),
    )



.. image-sg:: /_gallery/CatenaryCase/images/sphx_glr_run_catenary_001.png
   :alt: Catenary Final Shape
   :srcset: /_gallery/CatenaryCase/images/sphx_glr_run_catenary_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 47.772 seconds)


.. _sphx_glr_download__gallery_CatenaryCase_run_catenary.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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