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.
- Symbol:
G- Latex:
\(G\)
- Dimension:
any_dimension
- field¶
Any vector field, i.e. a vector-valued function that depends on the position vector.
- Symbol:
F- Latex:
\({\vec F}\)
- Dimension:
any_dimension
- curve¶
Curve along which the
circulationis calculated.- Symbol:
C- Latex:
\(C\)
- initial_parameter¶
Initial value of the curve parameter.
- Symbol:
u_1- Latex:
\(u_{1}\)
- Dimension:
dimensionless
- final_parameter¶
Final value of the curve parameter.
- Symbol:
u_2- Latex:
\(u_{2}\)
- Dimension:
dimensionless
- law¶
G = LineIntegral(dot(F, dr), C)- Latex:
- \[G = \int \limits_{C} \left( {\vec F}, d \vec r \right)\]