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

.. only:: html

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

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

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

.. _sphx_glr_examples_rigid_body_freefall.py:

Rigid body free fall — validation with NonLinear solver.

A rigid sphere falls under gravity. Compared with z(t) = z0 - 0.5*g*t^2.
Uses RigidBody + NonLinear (Fedoo's standard solver).

.. GENERATED FROM PYTHON SOURCE LINES 6-54




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

 .. code-block:: none

    ============================================================
    RIGID BODY FREE FALL — Fedoo validation
      m=1.0kg, z0=1.0m, dt=0.001s
    ============================================================
      z_final = -0.7658m (analytical: -0.7658m)
      error = 2.69e-14m
      PASS






|

.. code-block:: Python


    import time
    import numpy as np
    import pyvista as pv

    import fedoo as fd

    g = 9.81
    mass = 1.0
    radius = 0.1
    z0 = 1.0
    dt = 1e-3
    t_end = 0.6

    print("=" * 60)
    print("RIGID BODY FREE FALL — Fedoo validation")
    print(f"  m={mass}kg, z0={z0}m, dt={dt}s")
    print("=" * 60)

    space = fd.ModelingSpace("3D")
    space.new_variable("DispX")
    space.new_variable("DispY")
    space.new_variable("DispZ")
    space.new_vector("Disp", ("DispX", "DispY", "DispZ"))

    mesh = fd.Mesh.from_pyvista(
        pv.Sphere(radius=radius, center=(0, 0, z0), theta_resolution=8, phi_resolution=8)
    )
    body = fd.constraint.RigidBody(
        mesh,
        mass=mass,
        inertia_tensor=0.004 * np.eye(3),
        center_of_mass=np.array([0, 0, z0]),
    )
    body.set_force([0, 0, -mass * g])

    pb = body.solve(dt=dt, tmax=t_end, print_info=0)

    # Read trajectory from final state
    idx = body.assembly._dof_indices
    dof = pb.get_dof_solution()
    dz_final = dof[idx[2]]
    z_final = z0 + dz_final
    z_analytical = z0 - 0.5 * g * t_end**2

    print(f"  z_final = {z_final:.4f}m (analytical: {z_analytical:.4f}m)")
    print(f"  error = {abs(z_final - z_analytical):.2e}m")
    print(f"  {'PASS' if abs(z_final - z_analytical) < 0.01 else 'FAIL'}")


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

   **Total running time of the script:** (0 minutes 5.033 seconds)


.. _sphx_glr_download_examples_rigid_body_freefall.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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