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Aerodynamic Vector Autorotation Demo

Aerodynamic Vector Autorotation Demo
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2019-02-07 22:40
VectorCoordinate GeometryGeometric Construction
This example demonstrates the autorotation phenomenon of aerodynamic vectors under specific conditions, showcasing dynamic equilibrium. Key math concepts include vector operations, symmetry, equilateral triangle construction, coordinate geometry, and geometric transformations. Construction highlights from the summary involve commands like Line, Vector, Translate, and Circle. Suitable for high school students and researchers focusing on aerodynamics and geometric integration.

GeoGebra Commands & Parameters

  1. Line(A, Cp) → f
  2. OrthogonalLine(Cp, f) → g
  3. Point(g) → B
  4. Vector(Cp, B) → Vt
  5. Point(f) → C
  6. Vector(Cp, C) → Vi
  7. Translate(B, Vi) → B'
  8. Vector(B, B') → u
  9. Segment(C, B') → h
  10. Segment(B', B) → i
  11. Vector(Cp, B') → Vr
  12. Point(Circle[Cp, 5]) → Pas
  13. Segment(Cp, Pas) → j
  14. Ray(Pas, Cp) → Corde
  15. OrthogonalLine(Pas, Corde) → k
  16. Point(Corde) → D
  17. OrthogonalLine(D, Corde) → l
  18. Point(k) → E
  19. Line(E, Corde) → m
  20. Intersect(l, m) → F
  21. Point(Vr) → I
  22. Point(Corde) → J
  23. CircleArc(Cp, I, J) → c
  24. Point(Vt) → K
  25. Point(Corde) → L
  26. CircleArc(Cp, K, L) → d
  27. Length(c) → a
  28. PointIn(c) → Pointc
  29. Length(d) → b
  30. PointIn(d) → Pointd
  31. Angle(K, Cp, L) → α
  32. Angle(I, Cp, J) → β
  33. Line(Cp, Vr) → n
  34. Distance(Cp, n) → distanceCpn
  35. OrthogonalLine(Cp, n) → q
  36. Point(f) → O
  37. OrthogonalLine(Cp, n) → t
  38. Circle(Cp, ((CircleArc[Cp, I, J] * CircleArc[Cp, I, J]) * (Length[Vr] - Length[Vt]))) → e
  39. Intersect(e, n, 1) → G
  40. OrthogonalLine(G, n) → p
  41. Vector(Cp, G) → T
  42. Circle(Cp, (CircleArc[Cp, I, J] * (Length[Vr] - Length[Vt]))) → r
  43. OrthogonalLine(Cp, n) → s
  44. Intersect(r, s, 2) → H
  45. Vector(Cp, H) → P
  46. OrthogonalLine(H, p) → g_1
  47. Intersect(p, g_1) → M
  48. Vector(Cp, M) → Fr
  49. Segment(M, H) → h_1
  50. Segment(M, G) → i_1
  51. Ray(Cp, A) → f_1