|SimReal: Mathematics - Curve Integral - Div / Curl - Green|
Divergence and curl in a 2D vector field:
Vector field F: F = F(x,y) = [F1,F2] = [F1(x,y),F2(x,y)]
Closed curve C: r = r(t) = [r1,r2] = [r1(t) ,r2(t)]
As default the vector field is (this can be changed):
F = F(x,y) = [F1,F2] = [F1(x,y),F2(x,y)] = [-y,x]
As default the closed curve in the vector field is:
A square with the centre in origin and side equal 8.
Use the largest scrollbar at the bottom of the simulation window
to move a point along the closed curve (red color)
As you move along the curve, you can study the vector field
at the point position.
At the same time you can study the unit tangent vector, the unit normal vector
and the components of the vector field along these two unit vectors.
You can study the connection between single and double integrals
using Green's Theorem.
This is done by using the radiobuttons (1,2,3,4,5)
to select smaller and smaller areas inside the closed loop,
indicating going closer and closer to infinitesimal loops.
At the same time you can study (through formulaes) the use of Green's Theorem,
as you see the point moving around each of the small areas inside C.
Use the small scrollbar in the simulation window to see how the point
is moving around the current small area.
Click the 'Info' button for more information about the control buttons.