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Relativistic vs Galilean Velocity Addition

Relativistic vs Galilean Velocity Addition
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2016-08-15 11:34
VectorCalculusGeometric Construction
This example illustrates the difference between relativistic and Galilean velocity addition. Key mathematical concepts include vector addition. Using GeoGebra commands such as Circle, Segment, Vector, etc., the geometric meaning of different velocity additions is demonstrated. Suitable for high school physics and mathematics courses.

GeoGebra Commands & Parameters

  1. Circle(A, 3) → c
  2. Segment(A, B) → f
  3. Vector(A, B) → u
  4. Segment(A, C) → g
  5. Vector(A, C) → v
  6. OrthogonalLine(A, u, xOyPlane) → h
  7. OrthogonalLine(B, u, xOyPlane) → i
  8. Intersect(h, c, 1) → D
  9. Intersect(i, c, 2) → E
  10. Line(D, E) → j
  11. Intersect(h, c, 2) → F
  12. Intersect(i, c, 1) → G
  13. Line(F, G) → k
  14. Intersect(j, k) → H
  15. OrthogonalLine(A, v, xOyPlane) → l
  16. OrthogonalLine(C, v, xOyPlane) → m
  17. Intersect(m, c, 1) → I
  18. Intersect(l, c, 2) → J
  19. Line(I, J) → n
  20. Intersect(m, c, 2) → K
  21. Intersect(l, c, 1) → L
  22. Line(K, L) → p
  23. Intersect(n, g) → M
  24. Line(B, A) → q
  25. Line(C, A) → r
  26. Circle(A, M, xOyPlane) → d
  27. Intersect(r, d, 2) → N
  28. Intersect(c, q, 2) → O
  29. Intersect(c, q, 1) → P
  30. Circle(O, M, P) → e
  31. Intersect(r, d, 1) → W
  32. Line(W, H) → s
  33. Intersect(s, c, 2) → Q
  34. Intersect(s, c, 1) → R
  35. Circle(Q, A, R) → t
  36. Intersect(e, t, 2) → S
  37. Line(A, S) → a
  38. OrthogonalLine(A, a, xOyPlane) → b
  39. Intersect(b, c, 1) → T
  40. Line(T, S) → f_1
  41. Intersect(f_1, c, 1) → U
  42. Line(U, b) → g_1
  43. Intersect(a, g_1) → V
  44. Vector(A, V) → w
  45. Line(P, M) → h_1
  46. Line(B, h_1) → i_1
  47. Intersect(r, i_1) → Z
  48. Line(O, Z) → j_1
  49. Intersect(j_1, c, 1) → A_1
  50. CircleArc(A, P, A_1, xOyPlane) → c_1
  51. Line(C, u) → k_1
  52. Line(B, v) → l_1
  53. Intersect(k_1, l_1) → B_1
  54. Line(A, B_1) → m_1
  55. Vector(A, B_1) → u_1