.. _sphx_glr_api_gallery_classical_newtonian:

Newtonian mechanics
-------------------

Vector dynamics under a force: free fall with an oblique launch
velocity (:class:`~physicskit.classical.systems.newtonian.ProjectileMotion`) and the
2-body Kepler problem (:class:`~physicskit.classical.systems.newtonian.KeplerSystem`),
including the post-Newtonian and power-law perturbations that make
orbits precess, plus a pendulum viewed from Earth's rotating frame
(:class:`~physicskit.classical.systems.newtonian.FoucaultPendulum`), whose
Coriolis-driven swing-plane precession demonstrated that rotation
directly.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

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    <div class="sphx-glr-thumbcontainer" tooltip="ProjectileMotion is free fall under constant gravity g with an oblique initial velocity -- the historical &quot;cannonball&quot; problem. Without drag it is the separable Hamiltonian">

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  .. image:: /api/gallery/classical/newtonian/images/thumb/sphx_glr_plot_01_cannonball_thumb.png
    :alt:

  :doc:`/api/gallery/classical/newtonian/plot_01_cannonball`

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      <div class="sphx-glr-thumbnail-title">Free fall with an oblique velocity: the cannonball problem</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="KeplerSystem is the planar, reduced 2-body problem in the center-of-mass frame, a separable Hamiltonian in Cartesian coordinates q=(x,y), p=(p_x,p_y),">

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  .. image:: /api/gallery/classical/newtonian/images/thumb/sphx_glr_plot_02_kepler_precession_thumb.png
    :alt:

  :doc:`/api/gallery/classical/newtonian/plot_02_kepler_precession`

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      <div class="sphx-glr-thumbnail-title">Kepler orbits and perihelion precession</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="FoucaultPendulum models a small-oscillation pendulum&#x27;s horizontal displacement q=(x,y) (x = East, y = North) as seen from the rotating surface of the Earth. In a non-rotating (inertial) frame it would obey the isotropic harmonic equation \ddot q = -\omega_0^2 q, \omega_0 = \sqrt{g/\ell}; but Earth&#x27;s surface itself turns about the local vertical at rate \omega_z = \omega_\mathrm{earth}\sin(\text{latitude}), adding a velocity-dependent Coriolis term:">

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  .. image:: /api/gallery/classical/newtonian/images/thumb/sphx_glr_plot_03_foucault_pendulum_thumb.png
    :alt:

  :doc:`/api/gallery/classical/newtonian/plot_03_foucault_pendulum`

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      <div class="sphx-glr-thumbnail-title">The Foucault pendulum and Earth's rotation</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="plot_02_kepler_precession shows apsidal precession from the effective post-Newtonian c_\mathrm{pn}/r^3 correction. KeplerSystem has a second, independent perturbation family added to its radial potential:">

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  .. image:: /api/gallery/classical/newtonian/images/thumb/sphx_glr_plot_03_kepler_perturbations_thumb.png
    :alt:

  :doc:`/api/gallery/classical/newtonian/plot_03_kepler_perturbations`

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      <div class="sphx-glr-thumbnail-title">KeplerSystem's other perturbation: the power-law term</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="physicskit.classical.utils.conservation has more than just energy-drift helpers. angular_momentum_2d and angular_momentum_drift track the planar angular momentum">

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  .. image:: /api/gallery/classical/newtonian/images/thumb/sphx_glr_plot_04_conservation_diagnostics_thumb.png
    :alt:

  :doc:`/api/gallery/classical/newtonian/plot_04_conservation_diagnostics`

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      <div class="sphx-glr-thumbnail-title">Angular momentum: a different conservation law from energy</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Emmy Noether&#x27;s theorem ties each continuous symmetry of a system&#x27;s action to an exactly conserved quantity built from it: time-translation symmetry gives energy, rotational symmetry gives angular momentum. The Kepler problem carries a third, less obvious conserved quantity, the Laplace-Runge-Lenz vector">

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  .. image:: /api/gallery/classical/newtonian/images/thumb/sphx_glr_plot_05_noether_hidden_symmetry_thumb.png
    :alt:

  :doc:`/api/gallery/classical/newtonian/plot_05_noether_hidden_symmetry`

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      <div class="sphx-glr-thumbnail-title">Noether's Theorem and the Kepler Problem's Hidden Symmetry</div>
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    </div>


.. toctree::
   :hidden:

   /api/gallery/classical/newtonian/plot_01_cannonball
   /api/gallery/classical/newtonian/plot_02_kepler_precession
   /api/gallery/classical/newtonian/plot_03_foucault_pendulum
   /api/gallery/classical/newtonian/plot_03_kepler_perturbations
   /api/gallery/classical/newtonian/plot_04_conservation_diagnostics
   /api/gallery/classical/newtonian/plot_05_noether_hidden_symmetry