Acceleration from force and velocity
====================================

In special relativity, the Newton's second law does not hold in the classical form
:math:`\vec F = m \vec a`, but acceleration can still be expressed via force and velocity.

**Notation:**

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

**Conditions:**

#. This law applies to special relativity.

**Links:**

#. `Wikipedia, see paragraph <https://en.wikipedia.org/wiki/Acceleration_(special_relativity)#Acceleration_and_force>`__.

.. py:currentmodule:: symplyphysics.laws.relativistic.vector.acceleration_from_force_and_velocity

.. py:data:: acceleration

    Vector of the body's :attr:`~symplyphysics.symbols.classical_mechanics.acceleration`.

Symbol:
    :code:`a`

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

Dimension:
    :code:`acceleration`


.. py:data:: rest_mass

    :attr:`~symplyphysics.symbols.relativistic_mechanics.rest_mass` of the body.

Symbol:
    :code:`m_0`

Latex:
    :math:`m_{0}`

Dimension:
    :code:`mass`


.. py:data:: force

    Vector of the :attr:`~symplyphysics.symbols.classical_mechanics.force` exerted on the body.

Symbol:
    :code:`F`

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

Dimension:
    :code:`force`


.. py:data:: velocity

    Vector of the body's velocity. See :attr:`~symplyphysics.symbols.classical_mechanics.speed`.

Symbol:
    :code:`v`

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

Dimension:
    :code:`velocity`


.. py:data:: lorentz_factor

    :attr:`~symplyphysics.symbols.relativistic_mechanics.lorentz_factor`.

Symbol:
    :code:`gamma`

Latex:
    :math:`\gamma`

Dimension:
    :code:`dimensionless`


.. py:data:: law

    :code:`a = (F - dot(F, v) / c^2 * v) / (m_0 * gamma)`


    Latex:
        .. math::
            {\vec a} = \frac{{\vec F} - \frac{\left( {\vec F}, {\vec v} \right)}{c^{2}} {\vec v}}{m_{0} \gamma}