Circulation is integral along curve
===================================

The circulation of a vector field along a closed curve is defined via a curvilinear integral of
the field along the curve.

**Conditions:**

#. The parametrization of the curve is a vector function of one parameter that is continuously
   differentiable with respect to it.
#. The curve is closed.

.. py:currentmodule:: symplyphysics.laws.fields.circulation_is_integral_along_curve

.. py:data:: circulation

    Circulation of the vector :attr:`~field`.

Symbol:
    :code:`G`

Latex:
    :math:`G`

Dimension:
    :code:`any_dimension`


.. py:data:: field

    Any vector field, i.e. a vector-valued function that depends on the position vector.

Symbol:
    :code:`F`

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

Dimension:
    :code:`any_dimension`


.. py:data:: curve

    Curve along which the :attr:`~circulation` is calculated.

    Symbol:
        :code:`C`

    Latex:
        :math:`C`


.. py:data:: initial_parameter

    Initial value of the curve parameter.

Symbol:
    :code:`u_1`

Latex:
    :math:`u_{1}`

Dimension:
    :code:`dimensionless`


.. py:data:: final_parameter

    Final value of the curve parameter.

Symbol:
    :code:`u_2`

Latex:
    :math:`u_{2}`

Dimension:
    :code:`dimensionless`


.. py:data:: law

    :code:`G = LineIntegral(dot(F, dr), C)`


    Latex:
        .. math::
            G = \int \limits_{C} \left( {\vec F}, d \vec r \right)