Force from acceleration and velocity
====================================

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

**Conditions:**

#. This law applies to special relativity.

**Links:**

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

..
    TODO: rename file

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

.. 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:: 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:: tangential_acceleration

    Vector of the body's :attr:`~symplyphysics.symbols.classical_mechanics.acceleration` tangential to the :attr:`~velocity` vector.

Symbol:
    :code:`a_t`

Latex:
    :math:`{\vec a}_\text{t}`

Dimension:
    :code:`acceleration`


.. py:data:: normal_acceleration

    Vector of the body's :attr:`~symplyphysics.symbols.classical_mechanics.acceleration` normal to the :attr:`~velocity` vector.

Symbol:
    :code:`a_n`

Latex:
    :math:`{\vec a}_\text{n}`

Dimension:
    :code:`acceleration`


.. 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:`F = gamma^3 * m_0 * a_t + gamma * m_0 * a_n`


    Latex:
        .. math::
            {\vec F} = \gamma^{3} m_{0} {\vec a}_\text{t} + \gamma m_{0} {\vec a}_\text{n}