This applet is designed to build intuition about the curl of a vector field.
- The applet has a control window, a Vector Field window, and a Scaled Perp flow window.
- The control panel lets you define the vector field V=(p,q).
It gives readouts for the value of P0 along with V, and its curl, all evaluated at P0.
Vector Field window shows the the vector field V with a viewing window
centered around a point P0 whose coordinates are controlled by the
boxes and buttons of the control panel. The curl at P0 is
a vertical blue bar. A green circle of radius loopscale is
centered at the point. The loopvectors checkbox plots V at points
on this loop. Red arrows from the loop give the tangential component
control panel lets you set the viewing window along with the density
and scaling factor of the vector field. You can also scale the
size of the green circle and the length of the red vectors.
Scaled window sets up for the integral definition of curl.
(Recall that the divergence of V at P0 is the limit as R goes
to zero of the integral of the normal component of the flow
appropriatelty scaled for the lenght of the circle.) The
NormalFlowAntipodal window looks at the sum of the perpendicular
component of the
field at antipodal points. We would routinely expect the flow
much of the flow from antipodal points to cancel out, so that is