五球牛顿摆：对称碰撞与轨迹几何仿真

GeoGebra 命令及参数

1. Line(basePoint, zAxis) → j
2. Point(j) → heightController
3. Line(basePoint, yAxis) → g
4. Point(g) → widthController
5. Line(basePoint, xAxis) → f
6. Point(f) → lengthController
7. CircumcircleArc(trajectoryCenter_{3} + ((-pullRadius), 0, 0), trajectoryCenter_{3} + (0, 0, (-pullRadius)), trajectoryCenter_{3} + (pullRadius, 0, 0)) → e_2
8. Point(e_2) → pullPoint_{3}
9. Angle(pullPoint_{3}, trajectoryCenter_{3}, trajectoryCenter_{3} + restPosition, yAxis) → θ_{i}
10. CircumcircleArc(trajectoryCenter_{4} + ((-pullRadius), 0, 0), trajectoryCenter_{4} + (0, 0, (-pullRadius)), trajectoryCenter_{4} + (pullRadius, 0, 0)) → r_2
11. Point(r_2) → pullPoint_{4}
12. Angle(pullPoint_{4}, trajectoryCenter_{4}, trajectoryCenter_{4} + restPosition, yAxis) → φ_{i}
13. CircumcircleArc(trajectoryCenter_{2} + ((-pullRadius), 0, 0), trajectoryCenter_{2} + (0, 0, (-pullRadius)), trajectoryCenter_{2} + (pullRadius, 0, 0)) → d_2
14. Point(d_2) → pullPoint_{2}
15. CircumcircleArc(trajectoryCenter_{1} + ((-pullRadius), 0, 0), trajectoryCenter_{1} + (0, 0, (-pullRadius)), trajectoryCenter_{1} + (pullRadius, 0, 0)) → c_2
16. Point(c_2) → pullPoint_{1}
17. Angle(pullPoint_{1}, trajectoryCenter_{1}, trajectoryCenter_{1} + restPosition, yAxis) → γ_{i}
18. CircumcircleArc(trajectoryCenter_{5} + ((-pullRadius), 0, 0), trajectoryCenter_{5} + (0, 0, (-pullRadius)), trajectoryCenter_{5} + (pullRadius, 0, 0)) → s_2
19. Point(s_2) → pullPoint_{5}
20. Angle(pullPoint_{5}, trajectoryCenter_{5}, trajectoryCenter_{5} + restPosition, yAxis) → ω_{i}
21. Angle(pullPoint_{2}, trajectoryCenter_{2}, trajectoryCenter_{2} + restPosition, yAxis) → δ_{i}
22. Line(widthController, f) → h
23. Line(lengthController, g) → i
24. Intersect(i, h) → D
25. Polygon(basePoint, lengthController, D, widthController) → q1, a, b, d, c
26. Cylinder(J, K, cylinderRadius) → e, k, p, l
27. Cylinder(M, L, cylinderRadius) → m, q, r, n
28. Cylinder(H, J, cylinderRadius) → o, s, t, u
29. Cylinder(F, K, cylinderRadius) → v, c_1, d_1, w
30. Cylinder(E, L, cylinderRadius) → a_1, e_1, f_1, b_1
31. Cylinder(G, M, cylinderRadius) → g_1, g_2, g_3, g_4
32. Cylinder(F, E, cylinderRadius) → h_1, k_1, p_1, i_1
33. Cylinder(G, H, cylinderRadius) → j_1, q_1, r_1, l_1
34. If(time ≤ π / 2, trajectoryCenter_{1} + dynamicPosition_{1}, trajectoryCenter_{1} + dynamicPosition_{5}) → sphereCenter_{1}
35. Segment(U, sphereCenter_{1}) → f_2
36. Segment(sphereCenter_{1}, V) → h_2
37. If(time ≤ π / 2, trajectoryCenter_{2} + dynamicPosition_{2}, trajectoryCenter_{2} + dynamicPosition_{4}) → sphereCenter_{2}
38. Segment(Z, sphereCenter_{2}) → i_2
39. Segment(sphereCenter_{2}, W) → j_2
40. Segment(sphereCenter_{3}, A_1) → k_2
41. Segment(sphereCenter_{3}, B_1) → l_2
42. If(time ≤ π / 2, trajectoryCenter_{4} + dynamicPosition_{4}, trajectoryCenter_{4} + dynamicPosition_{2}) → sphereCenter_{4}
43. Segment(D_1, sphereCenter_{4}) → m_2
44. Segment(sphereCenter_{4}, C_1) → n_2
45. If(time ≤ π / 2, trajectoryCenter_{5} + dynamicPosition_{5}, trajectoryCenter_{5} + dynamicPosition_{1}) → sphereCenter_{5}
46. Segment(E_1, sphereCenter_{5}) → p_2
47. Segment(sphereCenter_{5}, F_1) → q_2
48. Sphere(sphereCenter_{1}, sphereRadius) → m_1
49. Sphere(sphereCenter_{2}, sphereRadius) → n_1
50. Sphere(sphereCenter_{3}, sphereRadius) → o_1
51. Sphere(sphereCenter_{4}, sphereRadius) → s_1
52. Sphere(sphereCenter_{5}, sphereRadius) → t_1