Magnus Effect on Balloon Trajectory

GeoGebra Commands & Parameters

1. Vector(B_1, Y) → v
2. Vector(B_1, X) → u
3. Vector(B_1, Z) → w
4. OrthogonalLine(View3D, yAxis) → a
5. OrthogonalLine(View3D, xAxis) → b
6. Translate(O, Vector[(8 * v)]) → OO
7. Segment(O, OO) → d
8. Translate(O, u) → O'
9. Mirror(O', O) → O''
10. Segment(O'', O') → e
11. Line(OO, e) → h
12. Line(O'', d) → i
13. Line(O', d) → j
14. Intersect(i, h) → A
15. Intersect(j, h) → B
16. Mirror(OO, A) → C
17. Mirror(OO, B) → D
18. Segment(E, F) → l
19. Segment(E, A) → m
20. Segment(F, B) → n
21. Polygon(C, D, H, G) → poly1, c_1, d_1, h_1, g_1
22. Mirror(OO, C) → I
23. Mirror(OO, D) → J
24. Mirror(OO, I) → K
25. Mirror(OO, J) → L
26. Line(L, j) → p
27. Line(M, h) → q
28. Line(K, i) → r
29. Intersect(q, r) → N
30. Line(P, h) → s
31. Mirror(L, P) → L'
32. Intersect(s, r) → Q
33. Line(L', s) → a_1
34. Intersect(a_1, r) → R
35. Polygon(R, N, M, L') → poly2, r_1, n_1, m_1, l'
36. Midpoint(Q, P) → S_1
37. Polygon(R, K, L, L') → poly3, r_2, k_2, l_1, l'_1
38. Line(O', O'') → b_1
39. Line(V, h) → e_1
40. Intersect(r_1, e_1) → T
41. Intersect(m_1, e_1) → U
42. Segment(T, U) → f_1
43. Point(f_1) → S
44. Vector(S, OO) → z
45. Sequence((x(S), y(S)) + (i / Distance * z) + (w * ((i * tan(α)) - ((0.5 * g / (((v_0 / 10)^(2) * cos(α)^(2)))) * i^(2)))), i, 0, Shoot, 0.1) → liste1
46. Sequence((x(S), y(S)) + (i / Distance * z) + (w * ((i * tan(α)) - ((0.5 * g / (((v_0 / 10)^(2) * cos(α)^(2)))) * i^(2)))) + (u * ((i * tan(Effet)) - ((0.5 * g / (((v_0 / 10)^(2) * cos(Effet)^(2)))) * i^(2)))), i, 0, Shoot, 0.1) → liste2
47. Midpoint(h_1) → W
48. CurveCartesian(x(K + ((0.5 * cos(i)) * u) - ((0.5 * sin(i)) * v)), y(K + ((0.5 * cos(i)) * u) - ((0.5 * sin(i)) * v)), i, 0, 1.5707963267948966) → o
49. CurveCartesian(x(L - ((0.5 * cos(i)) * u) - ((0.5 * sin(i)) * v)), y(L - ((0.5 * cos(i)) * u) - ((0.5 * sin(i)) * v)), i, 0, 1.5708) → i_1
50. Line(I, i) → j_1
51. Line(J, j) → p_1
52. Line(A_1, k_2) → q_1
53. Intersect(j_1, q_1) → C_1
54. Intersect(p_1, q_1) → D_1
55. Intersect(j_1, f_1) → E_1
56. Segment(I, C_1) → s_1
57. Segment(C_1, D_1) → t_1
58. Segment(D_1, J) → a_2
59. Midpoint(W, A_1) → F_1
60. CurveCartesian(x(A_1 + ((1.5 * cos(i)) * u) - (sin(i) * v)), y(A_1 + ((1.5 * cos(i)) * u) - (sin(i) * v)), i, 0, 3.141592653589793) → o_1
61. CurveCartesian(x(S_1 + ((2.5 * cos(i)) * u) - ((2.5 * sin(i)) * v)), y(S_1 + ((2.5 * cos(i)) * u) - ((2.5 * sin(i)) * v)), i, 0, 6.28319) → u_1
62. Segment(Q, P) → b_2
63. Segment(F, K_1) → c_2
64. Segment(H_1, E) → f_2
65. Polygon(K_1, I_1, G_1, H_1) → poly4, k_3, i_2, g_2, h_2
66. Intersect(h_2, k_3) → L_1
67. Intersect(n, c_1) → M_1
68. Polygon(L_1, F, M_1, I_1) → poly5, l_2, f_3, m_2, i_3
69. Intersect(m, c_1) → O_1
70. Polygon(H_1, E, O_1, G_1) → poly6, d_2, e_2, j_2, n_2
71. CurveCartesian(x(S + (i / Distance * z) + (w * ((i * tan(α)) - ((0.5 * g / (((v_0 / 10)^(2) * cos(α)^(2)))) * i^(2))))), y(S + (i / Distance * z) + (w * ((i * tan(α)) - ((0.5 * g / (((v_0 / 10)^(2) * cos(α)^(2)))) * i^(2))))), i, 0, Shoot) → v_1
72. CurveCartesian(x(S + (i / Distance * z) + (w * ((i * tan(α)) - ((0.5 * g / (((v_0 / 10)^(2) * cos(α)^(2)))) * i^(2)))) + (u * ((i * tan(Effet)) - ((0.5 * g / (((v_0 / 10)^(2) * cos(Effet)^(2)))) * i^(2))))), y(S + (i / Distance * z) + (w * ((i * tan(α)) - ((0.5 * g / (((v_0 / 10)^(2) * cos(α)^(2)))) * i^(2)))) + (u * ((i * tan(Effet)) - ((0.5 * g / (((v_0 / 10)^(2) * cos(Effet)^(2)))) * i^(2))))), i, 0, Shoot) → w_1