Coordinate conversion at constant velocity
==========================================

Let the frame of reference move relative to the other frame of reference at a constant speed along the X
axis, and the origin of the spatial coordinates coincide at the initial moment of time in both systems.
Then there are simple transformations that can be used to get the x coordinate in one frame of reference,
knowing the x coordinate in another frame of reference.

**Notation:**

#. :math:`c` (:code:`c`) is :attr:`~symplyphysics.quantities.speed_of_light`.

**Links:**

#. `Wikipedia, second formula in box <https://en.wikipedia.org/wiki/Lorentz_transformation#Coordinate_transformation>`__.

..
    TODO rename file

.. py:currentmodule:: symplyphysics.laws.relativistic.coordinate_conversion_velocity_constant

.. py:data:: position_in_proper_frame

    :attr:`~symplyphysics.symbols.classical_mechanics.position` in the second frame of reference.

Symbol:
    :code:`x_2`

Latex:
    :math:`x_{2}`

Dimension:
    :code:`length`


.. py:data:: position_in_lab_frame

    :attr:`~symplyphysics.symbols.classical_mechanics.position` in the first frame of reference.

Symbol:
    :code:`x_1`

Latex:
    :math:`x_{1}`

Dimension:
    :code:`length`


.. py:data:: proper_frame_speed_in_lab_frame

    :attr:`~symplyphysics.symbols.classical_mechanics.speed` of the second reference frame relative to the first one.

Symbol:
    :code:`v`

Latex:
    :math:`v`

Dimension:
    :code:`velocity`


.. py:data:: time_in_lab_frame

    :attr:`~symplyphysics.symbols.basic.time` in the first frame of reference.

Symbol:
    :code:`t_1`

Latex:
    :math:`t_{1}`

Dimension:
    :code:`time`


.. py:data:: law

    :code:`x_2 = (x_1 - v * t_1) / sqrt(1 - (v / c)^2)`


    Latex:
        .. math::
            x_{2} = \frac{x_{1} - v t_{1}}{\sqrt{1 - \left(\frac{v}{c}\right)^{2}}}