Relative acceleration from force
================================

Suppose reference frame :math:`S` is fixed to a moving object (e.g. Earth). For some body
:math:`B` we can write an equation of motion in coordinates of :math:`S'` akin to the Newton's
second law of motion for inertial frames, although we obtain two additional components to the
equation: one corresponding to the Coriolis force, and another to the fictitious force of
translation between inertial frame :math:`S` and non-inertial frame :math:`S'`.

**Links:**

#. `Wikipedia, derivable from here <https://en.wikipedia.org/wiki/Coriolis_force#Formula>`__.

.. py:currentmodule:: symplyphysics.laws.dynamics.vector.relative_acceleration_from_force

.. py:data:: relative_acceleration

    Vector of relative :attr:`~symplyphysics.symbols.classical_mechanics.acceleration` of body :math:`B` relative to :math:`S'`

Symbol:
    :code:`a_rel`

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

Dimension:
    :code:`acceleration`


.. py:data:: force

    Vector of the net physical :attr:`~symplyphysics.symbols.classical_mechanics.force` exerted on body :math:`B`.

Symbol:
    :code:`F`

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

Dimension:
    :code:`force`


.. py:data:: mass

    :attr:`~symplyphysics.symbols.basic.mass` of body :math:`B`.

Symbol:
    :code:`m`

Latex:
    :math:`m`

Dimension:
    :code:`mass`


.. py:data:: coriolis_acceleration

    Vector of the Coriolis :attr:`~symplyphysics.symbols.classical_mechanics.acceleration` of body :math:`B`.

    ..
        TODO: add link to vector law

Symbol:
    :code:`a_Cor`

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

Dimension:
    :code:`acceleration`


.. py:data:: translation_acceleration

    Vector of translation :attr:`~symplyphysics.symbols.classical_mechanics.acceleration` of body :math:`B`.

    ..
        TODO: add link to vector law

Symbol:
    :code:`a_tr`

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

Dimension:
    :code:`acceleration`


.. py:data:: law

    :code:`a_rel = F / m + a_Cor - a_tr`


    Latex:
        .. math::
            {\vec a}_\text{rel} = \frac{{\vec F}}{m} + {\vec a}_\text{Cor} - {\vec a}_\text{tr}