.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "api/gallery/classical/visualizers/plot_01_side_by_side_animation.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_visualizers_plot_01_side_by_side_animation.py: SideBySideAnimator: physical space + phase/energy diagnostics, live ========================================================================== The three animation helpers in ``physicskit.classical.visualizers.animations`` and ``physicskit.classical.visualizers.modal_analysis``, applied to three already-familiar conservative systems, each paired with a live diagnostic of its own governing physics: a double pendulum (:class:`~physicskit.classical.systems.lagrangian.DoublePendulum`, governed by its Euler-Lagrange equations of motion) shown with its physical rods next to a growing :math:`(\theta_1, \dot\theta_1)` phase trace; a precessing Kepler orbit (:class:`~physicskit.classical.systems.newtonian.KeplerSystem`, whose post-Newtonian term :math:`c_\mathrm{pn}/r^3` in :math:`V(r)` drives the precession) shown with its orbital path next to a growing energy trace; and a non-linear lattice chain (:class:`~physicskit.classical.systems.chains.FPUTChain`) shown via its live modal-energy bar chart :math:`E_k(t)`. .. GENERATED FROM PYTHON SOURCE LINES 22-49 .. code-block:: Python from physicskit.classical.systems.chains import FPUTChain from physicskit.classical.systems.lagrangian import DoublePendulum from physicskit.classical.systems.newtonian import KeplerSystem from physicskit.classical.visualizers.animations import orbit_trace_animation, pendulum_animation from physicskit.classical.visualizers.modal_analysis import animate_modal_energies def build_pendulum_animation(stride=500): pendulum = DoublePendulum([2.0, 1.0], [0.5, -0.3]) result = pendulum.integrate((0, 3.0), dt=1e-1, method="implicit_midpoint") side_by_side = pendulum_animation(result, pendulum.positions, mode="phase", stride=stride, figsize=(9, 4)) return side_by_side.build(interval=30) def build_orbit_animation(stride=20): kepler = KeplerSystem.from_orbital_elements(a=1.0, e=0.4) result = kepler.integrate((0, 20), dt=1e-1, method="yoshida4") side_by_side = orbit_trace_animation(result, mode="energy", stride=stride, figsize=(9, 4)) return side_by_side.build(interval=30) def build_modal_energy_animation(stride=10): chain = FPUTChain(n=16, beta=0.7, mode=1, amplitude=0.5) result = chain.integrate((0, 400), dt=0.1, method="yoshida4") return animate_modal_energies(chain, result, stride=stride) .. GENERATED FROM PYTHON SOURCE LINES 50-52 Double pendulum: physical rods + growing phase trace ------------------------------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 52-55 .. code-block:: Python pendulum_anim = build_pendulum_animation() .. container:: sphx-glr-animation .. raw:: html

.. GENERATED FROM PYTHON SOURCE LINES 56-58 Precessing Kepler orbit: orbital path + growing energy trace ------------------------------------------------------------------ .. GENERATED FROM PYTHON SOURCE LINES 58-61 .. code-block:: Python orbit_anim = build_orbit_animation() .. container:: sphx-glr-animation .. raw:: html

.. GENERATED FROM PYTHON SOURCE LINES 62-64 Lattice chain: live modal-energy bar chart ----------------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 64-66 .. code-block:: Python modal_anim = build_modal_energy_animation() .. container:: sphx-glr-animation .. raw:: html

.. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 20.551 seconds) .. _sphx_glr_download_api_gallery_classical_visualizers_plot_01_side_by_side_animation.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_01_side_by_side_animation.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_01_side_by_side_animation.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_01_side_by_side_animation.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_