行星轨道模拟2a:多体运动与几何构造

行星轨道模拟2a:多体运动与几何构造
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2020-06-27 08:28
该范例演示了围绕多个行星的轨道运动,通过动态几何方式展示天体运行轨迹与相关几何关系。核心数学概念包括圆、圆锥曲线、坐标几何、向量平移以及减法运算,同时涉及分布与二项分布等统计元素,但主体仍是几何构造与运动模拟。作图要点:使用GeoGebra命令如Point、Segment、Polygon、Slope、Circle、Area、PointIn、Line、Intersect、Name、Midpoint、Vector、Translate等,构建了多个点、线段、多边形、圆及向量对象,并通过滑块或参数控制轨道变化。适合中学数学或物理课程中用于演示行星运动、几何变换与坐标关系,也可用于探索圆锥曲线与统计分布的交叉应用。

GeoGebra 命令及参数

  1. Point(b) → A
  2. Point(c) → B
  3. Segment(C, A) → d
  4. Segment(C, B) → f
  5. Point(c) → D
  6. Segment(B, D) → i
  7. Point(Circle[A, 1.4142135623730951]) → F
  8. Segment(A, F) → g
  9. Segment(A, F) → h
  10. Polygon(B, C, D) → poly1, d_1, b_1, c_1
  11. Segment(C, D) → d_h
  12. Point(c) → E
  13. Point(c) → G
  14. Segment(B, G) → τ
  15. Segment(F, G) → n
  16. Slope(n) → m
  17. Slope(d_h) → m_1
  18. Circle(C, A) → k
  19. Area(k) → e
  20. PointIn(k) → Pointk
  21. Line(H, f) → j
  22. Intersect(k, j, 2) → I
  23. Segment(C, I) → l
  24. Line(I, b) → p
  25. Intersect(p, d) → J
  26. Segment(C, J) → q
  27. Segment(J, I) → s
  28. Point(s) → K
  29. Segment(C, K) → t
  30. Segment(I, F) → a_1
  31. Segment(J, A) → e_1
  32. Polygon(C, I, F, G, B) → poly2, c_2, i_1, f_1, g_1, b_2
  33. Name(o) → A1
  34. Name(u) → B1
  35. Name(a) → C1
  36. Point(k) → L
  37. Circle(M, N) → h_1
  38. Point(h_1) → O
  39. Point(h_1) → P
  40. Midpoint(O, P) → Q
  41. Segment(M, O) → j_1
  42. Segment(z_1, z_2) → k_1
  43. Vector(T, U) → v
  44. Translate(z_1, v) → z_3
  45. Translate(z_2, v) → z_4
  46. Segment(z_3, z_4) → l_1
  47. Point(l_1) → V
  48. Segment(V, W) → n_1
  49. Segment(V, Z) → p_1
  50. Segment(V, A_1) → q_1
  51. Segment(V, B_1) → r_1
  52. Segment(V, C_1) → s_1
  53. Segment(V, D_1) → t_1
  54. Segment(V, E_1) → a_2
  55. Segment(V, F_1) → d_2
  56. Segment(V, G_1) → e_2
  57. Point(j_1) → H_1
  58. Circle(H_1, I_1) → f_2
  59. Circle(H_1, J_1) → g_2
  60. Circle(H_1, K_1) → h_2
  61. Circle(H_1, L_1) → k_2
  62. Circle(H_1, M_1) → p_2
  63. Circle(H_1, N_1) → q_2
  64. Circle(H_1, O_1) → r_2
  65. Point(h_1) → P_1
  66. Circle(H_1, P_1) → s_2
  67. Segment(V, Q_1) → i_2