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Physics Problem: Separable Differential Equations by Earl Samuelson

Physics Problem: Separable Differential Equations by Earl Samuelson
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2016-03-29 23:46
VectorFunctionCalculusGeometric ConstructionGraphing
This example demonstrates how to graph the solution curves of separable differential equations using GeoGebra. It involves core mathematical concepts such as differential equations, separation of variables, function graphs, vectors, and three-dimensional space. Key GeoGebra commands and objects used in the construction include Intersect, Point, Segment, Polygon, Circle, OrthogonalLine, and Vector. Suitable for high school students and above to learn and understand the application of differential equations in physics problems, or for teaching demonstrations.

GeoGebra Commands & Parameters

  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