物理问题:可分微分方程

物理问题:可分微分方程
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2016-03-29 23:41
这个范例演示了一个物理问题,通过可分微分方程来描述。核心数学概念包括微分方程和可分方程。使用了Intersect, Point, Segment, Polygon, Circle, OrthogonalLine, Vector等GeoGebra命令进行构造。适合高中物理和数学课程使用。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Point(yAxis) → B
  3. Segment((5, 0), (5, 2)) → g
  4. Segment((0, 0), (0, 2)) → f
  5. Segment(B, D) → a_2
  6. Polygon(A, B, D, E) → poly1, a_1, b_2, d, e
  7. Intersect(p, c, (11.32455531795991, 1.5032515232604737E-9)) → C
  8. Intersect(p, c, (11.32455531795991, 1.5032515232604737E-9)) → F
  9. Intersect(i, j) → G
  10. Intersect(i, k) → H
  11. Segment(H, G) → l
  12. Intersect(p, m, (10.916079783099388, 0.250000000000135)) → I
  13. Intersect(k, m) → J
  14. Segment(J, I) → n
  15. Intersect(m, g) → K
  16. Segment(K, I) → q
  17. Intersect(h, r, (2, 1.75)) → L
  18. Intersect(p, r, (7.1713, 1.7642728155)) → M
  19. Circle(M, 0.25) → t
  20. Point(Circle[(0, 1.75), 5]) → N
  21. Segment(K, I) → b_1
  22. Segment(E, O) → d_1
  23. Intersect(r, a_2) → Q
  24. Circle(Q, 0.25) → c_1
  25. Circle(Q, 0.26867087944031054) → g_1
  26. OrthogonalLine(M, d_1) → h_1
  27. Intersect(h_1, d_1) → R
  28. Segment(R, M) → i_1
  29. OrthogonalLine(C, xAxis) → j_1
  30. OrthogonalLine(I, j_1) → k_1
  31. OrthogonalLine(I, xAxis) → l_1
  32. Intersect(c, l_1) → S
  33. Segment(S, I) → m_1
  34. Segment((5, 2), (a, 2)) → n_1
  35. Intersect(r, n_1) → T
  36. Circle(T, 0.25) → q_1
  37. Circle(T, 0.23573262929063565) → r_1
  38. Vector((5, 2), (a, 2)) → u_1
  39. Vector((a, 2), (a, 0.25)) → v_1
  40. Vector((5, 2), (a, 0.25)) → w_1
  41. Point(u_3) → U
  42. Segment(U, T) → u_2
  43. Segment(U, M) → w_2
  44. Segment(T, M) → v
  45. Segment((2, 1.75), N) → s_1
  46. Segment(P, V) → b
  47. Polygon(P, N, E, V) → poly2, p_1, n_2, e_1, v_2
  48. OrthogonalLine(M, f_1) → c_2
  49. Intersect(f_1, c_2) → W
  50. Circle(W, 0.25) → d_2
  51. Circle(W, 0.23702296356931926) → e_2
  52. Point(Circle[(2, 0), 12]) → Z
  53. Segment((2, 0), Z) → f_2
  54. Segment(D, M) → w
  55. Segment(D, T) → t_1
  56. Segment(D, T) → g_2
  57. OrthogonalLine(M, d_1) → h_2
  58. Intersect(h_2, d_1) → A_1
  59. Segment(A_1, M) → i_2
  60. Point(Circle[(5, 2), i_2]) → B_1
  61. Segment((5, 2), B_1) → u

AI 绘图提示语参考

画一个坐标系,在x轴和y轴上标出交点,然后从点(5,0)到(5,2)画一条水平线段,从(0,0)到(0,2)画一条垂直线段,连接这两条线段与y轴上的另一点形成一个四边形。再在四边形内部画一个圆,圆心在(7.1713, 1.7642728155),半径为0.25。在圆上标出几个点,并连接这些点形成闭合图形。最后,从圆心向x轴和y轴分别画垂线,并在垂线上标出交点,连接这些交点形成新的图形。
以上提示语为根据原始绘图命令整理而来,仅供参考。