圆与正方形的通量与环流

GeoGebra 命令及参数

1. CurveCartesian((Radius * cos(((2 * π) * t))) + x(Drag), (Radius * sin(((2 * π) * t))) + y(Drag), t, 0, 1) → path_c
2. Sequence(Sequence[Vector[(j, k), (j + (scale * F_1(j, k)), k + (scale * F_2(j, k)))], j, xmin, xmax, xstep], k, ymin, ymax, ystep) → vField
3. Line(I, xAxis) → f
4. Line(J, xAxis) → g
5. Line(K, xAxis) → h
6. Sequence(Segment[Rotate[curlPt - (0.2, 0), k + curlAngle, curlPt], Rotate[curlPt + (0.2, 0), k + curlAngle, curlPt]], k, 0, 2.0944, 1.0472) → spokes
7. Circle(divPt, 0.2) → divGlowCircle
8. CurveCartesian((t * x(Drag)) + ((1 - t) * x(Drag)), (t * (y(Drag) + Side)) + ((1 - t) * y(Drag)), t, 0, 1) → path_{s1}
9. CurveCartesian((t * (x(Drag) - Side)) + ((1 - t) * x(Drag)), (t * (y(Drag) + Side)) + ((1 - t) * (y(Drag) + Side)), t, 0, 1) → path_{s2}
10. CurveCartesian((t * (x(Drag) - Side)) + ((1 - t) * (x(Drag) - Side)), (t * y(Drag)) + ((1 - t) * (y(Drag) + Side)), t, 0, 1) → path_{s3}
11. CurveCartesian((t * x(Drag)) + ((1 - t) * (x(Drag) - Side)), (t * y(Drag)) + ((1 - t) * y(Drag)), t, 0, 1) → path_{s4}
12. Derivative(path_{s1}) → Dpath_{s1}
13. Derivative(path_{s2}) → Dpath_{s2}
14. Derivative(path_{s3}) → Dpath_{s3}
15. Derivative(path_{s4}) → Dpath_{s4}
16. Sum(Sequence[(((F_1(x(path_{s1}(i + dS / 2)), y(path_{s1}(i + dS / 2))), F_2(x(path_{s1}(i + dS / 2)), y(path_{s1}(i + dS / 2)))) * (y(Dpath_{s1}(i + dS / 2)), (-x(Dpath_{s1}(i + dS / 2))))) * dS), i, 0, 1 - dS, dS]) → Flux_{s1}
17. Sum(Sequence[(((F_1(x(path_{s2}(i + dS / 2)), y(path_{s2}(i + dS / 2))), F_2(x(path_{s2}(i + dS / 2)), y(path_{s2}(i + dS / 2)))) * (y(Dpath_{s2}(i + dS / 2)), (-x(Dpath_{s2}(i + dS / 2))))) * dS), i, 0, 1 - dS, dS]) → Flux_{s2}
18. Sum(Sequence[(((F_1(x(path_{s3}(i + dS / 2)), y(path_{s3}(i + dS / 2))), F_2(x(path_{s3}(i + dS / 2)), y(path_{s3}(i + dS / 2)))) * (y(Dpath_{s3}(i + dS / 2)), (-x(Dpath_{s3}(i + dS / 2))))) * dS), i, 0, 1 - dS, dS]) → Flux_{s3}
19. Sum(Sequence[(((F_1(x(path_{s4}(i + dS / 2)), y(path_{s4}(i + dS / 2))), F_2(x(path_{s4}(i + dS / 2)), y(path_{s4}(i + dS / 2)))) * (y(Dpath_{s4}(i + dS / 2)), (-x(Dpath_{s4}(i + dS / 2))))) * dS), i, 0, 1 - dS, dS]) → Flux_{s4}
20. Sum(list1, (s * 4)) → TT
21. Sum(Sequence[((path_{s1}(i + dS) - path_{s1}(i)) * (F_1(x(path_{s1}(i + dS / 2)), y(path_{s1}(i + dS / 2))), F_2(x(path_{s1}(i + dS / 2)), y(path_{s1}(i + dS / 2))))), i, 0, s - dS, dS]) → Circ_1
22. Sum(Sequence[((path_{s2}(i + dS) - path_{s2}(i)) * (F_1(x(path_{s2}(i + dS / 2)), y(path_{s2}(i + dS / 2))), F_2(x(path_{s2}(i + dS / 2)), y(path_{s2}(i + dS / 2))))), i, 0, s - dS, dS]) → Circ_2
23. Sum(Sequence[((path_{s3}(i + dS) - path_{s3}(i)) * (F_1(x(path_{s3}(i + dS / 2)), y(path_{s3}(i + dS / 2))), F_2(x(path_{s3}(i + dS / 2)), y(path_{s3}(i + dS / 2))))), i, 0, s - dS, dS]) → Circ_3
24. Sum(Sequence[((path_{s4}(i + dS) - path_{s4}(i)) * (F_1(x(path_{s4}(i + dS / 2)), y(path_{s4}(i + dS / 2))), F_2(x(path_{s4}(i + dS / 2)), y(path_{s4}(i + dS / 2))))), i, 0, s - dS, dS]) → Circ_4
25. Sum(list2, (4 * s)) → TT_2
26. Segment(path_{s1}(0.5), path_{s1}(0.5 + 0.01)) → arrw01
27. Segment(path_{s2}(0.5), path_{s2}(0.5 + 0.01)) → arrw02
28. Segment(path_{s3}(0.5), path_{s3}(0.5 + 0.01)) → arrw03
29. Segment(path_{s4}(0.5), path_{s4}(0.5 + 0.01)) → arrw04
30. Distance(Drag, (0, 0)) → cond
31. Polygon(Drag, M, 4) → poly1, i, j, k, l, N, O
32. Sum(Sequence[((path_c(i + dS) - path_c(i)) * (F_1(x(path_c(i + dS / 2)), y(path_c(i + dS / 2))), F_2(x(path_c(i + dS / 2)), y(path_c(i + dS / 2))))), i, 0, s2 - dS, dS]) → Circ
33. Derivative(path_c) → Dpath_c
34. Sum(Sequence[(((F_1(x(path_c(i + dS / 2)), y(path_c(i + dS / 2))), F_2(x(path_c(i + dS / 2)), y(path_c(i + dS / 2)))) * (y(Dpath_c(i + dS / 2)), (-x(Dpath_c(i + dS / 2))))) * dS), i, 0, s2 - dS, dS]) → Flux
35. Segment(path_c(0.3), path_c(0.3 + 0.01)) → arrow01
36. Segment(path_c(0.6), path_c(0.6 + 0.01)) → arrow02
37. CurveCartesian((Radius * cos(((2 * π) * t))) + x(Drag), (Radius * sin(((2 * π) * t))) + y(Drag), t, 0, s2) → partPath_c