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Piston Movement Equation Demo

Piston Movement Equation Demo
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2019-05-13 12:02
FunctionCoordinate GeometryCalculusDerivativeGeometric Construction
This example demonstrates the linear motion of a piston and its position function relationship. It involves core mathematical concepts such as derivatives, linear functions, tangent functions, and analytical geometry. Construction highlights include using commands like Line, Circle, Point, Distance, Intersect, Segment, Midpoint, Polygon, Mirror, Ray, OrthogonalLine, Angle, and Derivative in GeoGebra. Suitable for high school and above students studying calculus and mechanics in physics.

GeoGebra Commands & Parameters

  1. Line(O, xAxis) → f_1
  2. Circle(O, F_1) → e_1
  3. Point(e_1) → G
  4. Line(F_1, O) → a_1
  5. Distance(F_1, O) → dis
  6. Circle(G, dis) → e
  7. Point(e_1) → A
  8. Point(f_1) → B
  9. Line(O, B) → a
  10. Circle(A, 12) → c
  11. Intersect(c, a, 2) → C
  12. Segment(C, A) → b
  13. Circle(C, 4) → d
  14. Line(C, xAxis) → f
  15. Intersect(d, f, 1) → D
  16. Segment(D, C) → g
  17. Midpoint(b) → E
  18. Polygon(D, C, 4) → poly1, h, i, j, k, F, H
  19. Polygon(C, D, 4) → poly2, l, m, n, p, I, J
  20. Mirror(poly1, k) → poly1'
  21. Mirror(poly2, m) → poly2'
  22. Ray(F, H) → q
  23. Ray(J, I) → r
  24. Point(q) → K
  25. OrthogonalLine(K, q) → s
  26. Intersect(s, r) → L
  27. Line(M, j) → t
  28. Point(t) → N
  29. Line(N, k) → b_1
  30. Point(b_1) → P
  31. Line(P, t) → c_1
  32. OrthogonalLine(M, t) → d_1
  33. Intersect(c_1, d_1) → Q
  34. Segment(M, N) → g_1
  35. Segment(N, P) → h_1
  36. Segment(P, Q) → i_1
  37. Segment(O, A) → j_1
  38. Segment(C, A) → k_1
  39. Segment(C, O) → l_1
  40. Angle(C, O, A) → al
  41. Derivative(ff) → ff'
  42. Derivative(ff') → ff''