螺旋曲线上的正弦波与切线动画

GeoGebra 命令及参数

1. Line(A, xAxis) → n
2. Circle(A, R) → c
3. Intersect(c, n) → E, F
4. Point(c) → B
5. Circle(A, R + r) → d
6. Rotate(F, (t * w), A) → B'
7. Ray(A, B') → a
8. Intersect(d, a) → C,
9. Circle(C, B') → e
10. Rotate(B', (t * w1), C) → B''
11. Ray(C, B'') → b
12. Segment(C, B'') → i
13. Segment(A, B') → j
14. CurveCartesian(x(A) + ((R + r) * (cos((w * i)) + cos((w1 * i)))), y(A) + ((R + r) * (sin((w * i)) + sin((w1 * i)))), i, 0, t) → k
15. CurveCartesian(x(A) + ((R + r) * cos((w * i))) - (r * cos(((w1 + w) * i) + 3.141592653589793)), y(A) + ((R + r) * sin((w * i))) - (r * sin(((w1 + w) * i) + 3.141592653589793)), i, 0, t) → o
16. Ray(A, G) → s
17. CurveCartesian(x(A) + ((R + r) * cos((w * i))) - (r * cos(((w1 + w) * i))), y(A) + ((R + r) * sin((w * i))) - (r * sin(((w1 + w) * i))), i, 0, t) → l
18. CurveCartesian(x(G) + ((2 * π) * i), y(G) + ((R + r) * sin((w * i))) - (r * sin(((w1 + w) * i))), i, 0, t) → u
19. Segment(I, H) → f
20. Point(i) → D
21. Segment(I, D) → g
22. Intersect(e, j) → J, K
23. Segment(A, K) → h
24. Point(s) → L
25. Ray(G, L) → m
26. Sequence(G + (i, 0), i, 0, 160, 39.5 / 4) → l1
27. Sequence(G + (i, 0), i, 0, 160, 39.5) → l2
28. Sequence(Text[i / 2 + "π", l1(i + 1) - (2.5, 0.45), true, true], i, 4, 20, 4) → l4
29. Segment(G + (0, R + 5), G - (0, R + 5)) → r_{1}
30. Ray(A, K) → f_1
31. Intersect(c, f_1) → M,
32. Segment(A, M) → g_1
33. Segment(A, C) → h_1
34. Intersect(c, h_1) → N,
35. Segment(A, N) → i_1