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一般旋转场

一般旋转场
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2016-11-29 03:44
向量立体几何微积分导数积分
①本范例演示空间中一般旋转场的可视化与计算；②涉及核心数学概念包括向量场、导数、积分、立体几何；③构造中运用了Derivative, CurveCartesian, Point, Vector, Sequence, Line, Circle, Simplify等GeoGebra命令与对象；④适合高中及以上学生及数学爱好者学习向量微积分与空间几何应用。

GeoGebra 命令及参数

  1. Derivative(f, x) → Dfx
  2. Derivative(g, y) → Dgy
  3. Derivative(h, z) → Dhz
  4. Derivative(f, y) → Dfy
  5. Derivative(f, z) → Dfz
  6. Derivative(g, x) → Dgx
  7. Derivative(g, z) → Dgz
  8. Derivative(h, y) → Dhy
  9. Derivative(h, x) → Dhx
  10. CurveCartesian(xx(t), yy(t), zz(t), t, a, b) → myCurve
  11. Point(myCurve) → P
  12. Vector(P, P + fieldAtP) → fieldVectorAtP
  13. Vector(Q, Q + fieldAtQ) → fieldVectorAtQ
  14. Sequence(Sequence[Sequence[Vector[(i, j, k), (i, j, k) + (multiplier * (f(i, j, k), g(i, j, k), h(i, j, k)))], i, (-sampleSize), sampleSize, sampleStep], j, (-sampleSize), sampleSize, sampleStep], k, (-sampleSize), sampleSize, sampleStep) → myField
  15. CurveCartesian((a_1 * t), (a_2 * t), (a_3 * t), t, -5, 5) → axisOfRotation
  16. Point(axisOfRotation) → A
  17. Point(axisOfRotation) → B
  18. Line(B, A) → i
  19. Circle(B, r, i) → d
  20. Point(d) → C
  21. Vector(C, C + fieldAtC) → fieldVectorAtC
  22. Simplify(f) → fSimp
  23. Simplify(g) → gSimp
  24. Simplify(h) → hSimp