Acceleration due to non-uniform rotation
========================================

Imagine two reference frames, one of which is fixed (:math:`S`) and the other is moving
(:math:`S'`). When :math:`S'` rotates around :math:`S` in a non-uniform way, the acceleration of
some body :math:`B` in :math:`S` has a component corresponding to that non-uniform rotation of
:math:`S'`. It is part of the transfer acceleration of body :math:`B` in :math:`S`.

**Notation:**

#. :math:`\left[ \vec a, \vec b \right]` (:code:`cross(a, b)`) is vector product of
   :math:`\vec a` and :math:`\vec b`.

**Links:**

#. `Wikipedia <https://ru.wikipedia.org/wiki/%D0%A1%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D0%B5_%D0%B4%D0%B2%D0%B8%D0%B6%D0%B5%D0%BD%D0%B8%D0%B5#%D0%A3%D1%81%D0%BA%D0%BE%D1%80%D0%B5%D0%BD%D0%B8%D0%B5>`__.

..
    TODO find English link

.. py:currentmodule:: symplyphysics.classical_mechanics.kinematics.relative_motion.acceleration_due_to_non_uniform_rotation

.. py:data:: non_uniform_rotation_acceleration

    Vector of :attr:`~symplyphysics.symbols.classical_mechanics.acceleration` due to non-uniform rotation of :math:`S'` relative to :math:`S`.

Symbol:
    :code:`a_rot`

Latex:
    :math:`{\vec a}_\text{rot}`

Dimension:
    :code:`acceleration`


.. py:data:: time

    :attr:`~symplyphysics.symbols.basic.time`.

Symbol:
    :code:`t`

Latex:
    :math:`t`

Dimension:
    :code:`time`


.. py:data:: angular_velocity

    Pseudovector of the body's angular velocity as a function of :attr:`~time`. See
    :attr:`~symplyphysics.symbols.classical_mechanics.angular_speed`.

Symbol:
    :code:`w(t)`

Latex:
    :math:`{\vec \omega} \left( t \right)`

Dimension:
    :code:`angle/time`


.. py:data:: position_vector

    The body's position vector. See :attr:`~symplyphysics.symbols.classical_mechanics.distance_to_origin`.

Symbol:
    :code:`r`

Latex:
    :math:`{\vec r}`

Dimension:
    :code:`length`


.. py:data:: law

    :code:`a_rot = cross(Derivative(w(t), t), r)`


    Latex:
        .. math::
            {\vec a}_\text{rot} = \left[ \frac{d}{d t} {\vec \omega} \left( t \right), {\vec r} \right]