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General Rotation Field

General Rotation Field
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2016-11-29 03:44
VectorSolid GeometryCalculusDerivativeIntegral
This example demonstrates the visualization and calculation of a general rotation field in space. It involves core mathematical concepts like vector fields, derivatives, integrals, and solid geometry. GeoGebra commands and objects such as Derivative, CurveCartesian, Point, Vector, Sequence, Line, Circle, and Simplify are used in its construction. Suitable for high school students and mathematics enthusiasts learning vector calculus and spatial geometry applications.

GeoGebra Commands & Parameters

  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