.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "api/gallery/classical/rotations/plot_03_rigid_body_3d.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_api_gallery_classical_rotations_plot_03_rigid_body_3d.py: The Dzhanibekov effect, literally: a tumbling 3D rigid body ================================================================== The same torque-free rigid body as :doc:`plot_01_dzhanibekov` -- :class:`~physicskit.classical.systems.rotations.EulerTop`, governed by Euler's equations :math:`I_i\dot\omega_i = (I_j - I_k)\,\omega_j\omega_k` (cyclic in :math:`i,j,k`) for the body-frame angular velocity, coupled to the orientation quaternion. The SO(3) momentum-sphere picture (:doc:`plot_01_dzhanibekov`) shows the *abstract* geometry behind the intermediate axis theorem. This instead draws the actual rigid body -- a flattened "paddle" (book/phone-like) box, elongated along its smallest-moment axis and flattened along its largest-moment axis, exactly like the real object in the famous ISS video -- and rotates it in 3D with :func:`~physicskit.classical.visualizers.animations.animate_rigid_body_tumble`, which builds the wireframe box from ``half_extents`` and rotates its vertices at each frame via :meth:`~physicskit.classical.systems.rotations.EulerTop.rotation_matrix`, built from the integrated orientation quaternion. Spin it about the intermediate axis and it periodically flips end over end; spin it about either other principal axis and it just spins. .. GENERATED FROM PYTHON SOURCE LINES 27-37 .. code-block:: Python import matplotlib.pyplot as plt from physicskit.classical.systems.rotations import EulerTop from physicskit.classical.visualizers.animations import animate_rigid_body_tumble # Half-extents (a, b, c) along body axes (1, 2, 3): a > b > c makes # I1 = b^2+c^2 (smallest) < I2 = a^2+c^2 < I3 = a^2+b^2 (largest), # matching the EulerTop's I1=1, I2=2, I3=3 below. HALF_EXTENTS = (1.5, 1.0, 0.4) .. GENERATED FROM PYTHON SOURCE LINES 38-40 Spin about the intermediate axis: it periodically flips end over end -------------------------------------------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 40-48 .. code-block:: Python top = EulerTop(omega0=[0.01, 1.0, 0.01], I1=1.0, I2=2.0, I3=3.0) result = top.integrate((0, 30.0), dt=1e-3, method="implicit_midpoint") anim = animate_rigid_body_tumble(top, result, half_extents=HALF_EXTENTS, interval=50, stride=200) plt.show() .. container:: sphx-glr-animation .. raw:: html

.. GENERATED FROM PYTHON SOURCE LINES 49-53 To save the animation to a file instead of (or in addition to) displaying it interactively, use e.g.:: anim.save("rigid_body_tumble_animation.gif", writer="pillow", fps=30) .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 9.029 seconds) .. _sphx_glr_download_api_gallery_classical_rotations_plot_03_rigid_body_3d.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_03_rigid_body_3d.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_03_rigid_body_3d.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_03_rigid_body_3d.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_