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.classical_mechanics.kinematics.relative_motion.absolute_velocity_of_arbitrary_motion

.. py:data:: absolute_velocity

    Vector of velocity relative to fixed frame :math:`S`. See :attr:`~symplyphysics.symbols.classical_mechanics.speed`.

Symbol:
    :code:`v_abs`

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

Dimension:
    :code:`velocity`


.. py:data:: relative_velocity

    Vector of velocity relative to moving frame :math:`S'`. See :attr:`~symplyphysics.symbols.classical_mechanics.speed`.

Symbol:
    :code:`v_rel`

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

Dimension:
    :code:`velocity`


.. py:data:: transfer_velocity

    Vector of velocity due to movement of :math:`S'` relative to :math:`S`. See :attr:`~symplyphysics.symbols.classical_mechanics.speed`.

Symbol:
    :code:`v_tr`

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

Dimension:
    :code:`velocity`


.. py:data:: law

    :code:`v_abs = v_rel + v_tr`


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