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4D 3-Body Momentum Conservation Visualization

4D 3-Body Momentum Conservation Visualization
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2019-01-22 14:02
VectorSolid GeometryMatrixGeometric Construction
This example demonstrates the conservation of momentum in a 3-body system within a 4-dimensional space. Key math concepts include vectors and matrix operations. Construction highlights the use of GeoGebra commands and objects such as Rotate, Polygon, Midpoint, SVD, Segment, Intersect, LaTeX, Point, Sphere, and CircleArc. Suitable for high school students and math enthusiasts exploring high-dimensional physics and geometric transformations.

GeoGebra Commands & Parameters

  1. Rotate(Rotate[Rotate[A, α, xAxis], β, yAxis], γ, zAxis) → A'
  2. Rotate(Rotate[Rotate[B, α, xAxis], β, yAxis], γ, zAxis) → B'
  3. Rotate(Rotate[Rotate[C, α, xAxis], β, yAxis], γ, zAxis) → C'
  4. Polygon(A'norm, B'norm, C'norm) → poly2, c'norm, a'norm, b'norm
  5. Midpoint(b'norm) → M
  6. Midpoint(a'norm) → L
  7. SVD(H) → svd
  8. Segment(G, M) → h
  9. Segment(L, F) → g
  10. Intersect(h, g) → T
  11. Polygon(Anorm, Bnorm, Cnorm) → poly1, cnorm, anorm, bnorm
  12. LaTeX(R) → text4
  13. Midpoint(c'norm) → K
  14. Segment(K, I) → f
  15. Intersect(bnorm, cnorm) → N
  16. Intersect(anorm, cnorm) → O
  17. Intersect(bnorm, anorm) → P
  18. Point(zAxis) → Z
  19. Sphere(T, K) → sphereA
  20. CircleArc(T, L, M) → d
  21. CircleArc(T, M, K) → k
  22. CircleArc(T, K, L) → p
  23. Segment(Median1, O) → i
  24. Segment(Median1, N) → j
  25. Segment(Median1, P) → l
  26. Segment(Median2, I) → m
  27. Segment(Median2, G) → n
  28. Segment(Median2, F) → q
  29. Point(yAxis) → Y
  30. Point(xAxis) → X
  31. Sphere(T, r) → sphereB
  32. LaTeX(H, true, true) → text6