de-CH
utf-8
math math-format graphie interactive
Vector Fields: Finding Values
va-00-01
custom
1950
randRangeExclude(-6,6,[0,1]) randRangeExclude(-6,6,[0,1]) randRangeExclude(-6,6,[0,1]) randRangeExclude(-6,6,[0,1,B*C/A]) randRangeNonZero(-8,8) randRangeExclude(-4,4)
A *X + B*Y C *X + D*Y

Let K : \mathbb R^2 \to \mathbb R^2 be the plane vector field with K(x,y) = \begin{pmatrix} A x + B y \\ C x + Dy \end{pmatrix}.

Move the given point (a,b) to the endpoint of K(a,b).

style({ stroke: "black", strokeWidth: 2 }); graphInit({ range: [[-11, 11], [-9, 9]], scale: [22, 22], tickStep: 2, labelStep: 1, axisArrows: "->" }); label([-2,0], "\\llap{-}2", "below"); label([0,-2], "\\llap{-}2", "left"); label([9.5,0], "x", "above right"); label([0.1,7.5], "y", "above right"); addMouseLayer(); graph.point = addMovablePoint({ coord: [X , Y ], snapX: 1, snapY: 1 });

[ graph.point.coord ]
return ((guess[0][0] === X+P) && (guess[0][1] === Y+Q));
graph.point.setCoord(guess);

The given point has the coordinates (X , Y).

We substitute this in K(x,y) and compute K(X , Y)= (P , Q).

circle([X+P, Y+Q], 0.25, { fill: "blue" }); circle([X, Y], 0.25, { fill: "red" });

For the desired endpoint, we start at (X , Y) and then move according to K(X , Y)= (P , Q) along the x- and y-direction.

line( [X,Y], [X+P,Y+Q], { stroke: ORANGE, arrows: "->" });