Classical addition of velocities
================================

The *law of classical addition of velocities*, usually attributed to Galileo and called the
*Galilean law of velocity addition*, states that the velocity of a body in an inertial reference
frame :math:`A` can be found as a sum of its velocity in another inertial reference frame :math:`B` and the
velocity of frame :math:`B` relative to frame :math:`A`.

**Conditions:**

#. Velocity vectors must be collinear.
#. Space and time are absolute.
#. Applicable to inertial reference frames.

**Links:**

#. `Wikipedia, vector counterpart of this law <https://en.wikipedia.org/wiki/Velocity-addition_formula#Galilean_relativity>`__.

.. py:currentmodule:: symplyphysics.laws.kinematics.classical_addition_of_velocities

.. py:data:: body_speed_in_first_frame

    :attr:`~symplyphysics.symbols.classical_mechanics.speed` of the body in frame :math:`A`.

Symbol:
    :code:`v_OA`

Latex:
    :math:`v_{OA}`

Dimension:
    :code:`velocity`


.. py:data:: body_speed_in_second_frame

    :attr:`~symplyphysics.symbols.classical_mechanics.speed` of the body in frame :math:`B`.

Symbol:
    :code:`v_OB`

Latex:
    :math:`v_{OB}`

Dimension:
    :code:`velocity`


.. py:data:: second_frame_speed_in_first_frame

    :attr:`~symplyphysics.symbols.classical_mechanics.speed` of frame :math:`B` relative to frame :math:`A`.

Symbol:
    :code:`v_BA`

Latex:
    :math:`v_{BA}`

Dimension:
    :code:`velocity`


.. py:data:: law

    :code:`v_OA = v_OB + v_BA`


    Latex:
        .. math::
            v_{OA} = v_{OB} + v_{BA}