Absolute velocity of arbitrary motion
=====================================

Imagine two reference frames, one of which is fixed (:math:`S`) and the other one is moving arbitrarily (:math:`S'`). The motion of the
body relative to fixed frame :math:`S` is called *absolute motion*. The motion of the body relative to moving frame :math:`S'`
is called *relative motion*. The motion of the body due to the motion of reference frame :math:`S'` is called *transfer
motion*. Absolute velocity is the sum of relative and transfer velocities.

**Notes:**

#. Moving frame :math:`S'` can perform both translational and rotational motion.

**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%A1%D0%BA%D0%BE%D1%80%D0%BE%D1%81%D1%82%D1%8C>`__.

..
    TODO: find English link

.. py:currentmodule:: symplyphysics.laws.kinematics.vector.absolute_velocity_of_arbitrary_motion



.. py:function:: absolute_velocity_law(relative_velocity_, transfer_velocity_)

    Absolute velocity via relative and transfer velocities.

    Law:
        :code:`v_abs = v_rel + v_tr`

    Latex:
        .. math::
            {\vec v}_\text{abs} = {\vec v}_\text{rel} + {\vec v}_\text{tr}

    :param relative_velocity\_: velocity relative to moving frame :math:`S'`

        Symbol: :code:`v_rel`

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

        Dimension: *velocity*

    :param transfer_velocity\_: velocity due to movement of frame :math:`S'` relative to frame :math:`S`

        Symbol: :code:`v_tr`

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

        Dimension: *velocity*

    :return: velocity relative to fixed frame :math:`S`

        Symbol: :code:`v_abs`

        Latex: :math:`{\vec v}_\text{abs}`

        Dimension: *velocity*


.. py:function:: relative_velocity_law(absolute_velocity_, transfer_velocity_)

    Relative velocity via absolute and transfer velocities.

    Law:
        :code:`v_rel = v_abs - v_tr`

    Latex:
        .. math::
            {\vec v}_\text{rel} = {\vec v}_\text{abs} - {\vec v}_\text{tr}

    :param absolute_velocity\_: velocity relative to fixed frame :math:`S`

        Symbol: :code:`v_abs`

        Latex: :math:`{\vec v}_\text{abs}`

        Dimension: *velocity*
                
    :param transfer_velocity\_: velocity due to movement of frame :math:`S'` relative to frame :math:`S`

        Symbol: :code:`v_tr`

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

        Dimension: *velocity*

    :return: velocity relative to moving frame :math:`S'`

        Symbol: :code:`v_rel`

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

        Dimension: *velocity*


.. py:function:: transfer_velocity_law(absolute_velocity_, relative_velocity_)

    Transfer velocity via absolute and relative velocities.

    Law:
        :code:`v_tr = v_abs - v_rel`

    Latex:
        .. math::
            {\vec v}_\text{tr} = {\vec v}_\text{abs} - {\vec v}_\text{rel}

    :param absolute_velocity\_: velocity relative to fixed frame :math:`S`

        Symbol: :code:`v_abs`

        Latex: :math:`{\vec v}_\text{abs}`

        Dimension: *velocity*

    :param relative_velocity\_: velocity relative to moving frame :math:`S'`

        Symbol: :code:`v_rel`

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

        Dimension: *velocity*

    :return_: velocity due to movement of frame :math:`S'` relative to frame :math:`S`

        Symbol: :code:`v_tr`

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

        Dimension: *velocity*