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二维波形演示

二维波形演示
几何画板及绘图内容加载中，请稍等……
2017-10-09 07:06
向量函数参数方程几何作图
①本范例演示二维波形在平面上的传播与变化现象；②涉及的核心数学概念包括函数图像、参数方程、向量运算及几何变换；③构造要点：使用了GeoGebra命令Corner, CornerThreeD, Text, Textfield, Sequence，对象包括λ_1, A_{2D}, A_{3D}, f_1, s_1, time, ShiftS, tMax, o, G1Corner系列, G2Corner系列, G3DCorner系列, G2Text系列, TabWaveA等，用于动态展示波形参数与几何关系；④适合高中及以上数学、物理学生及教师用于教学演示与探究。

GeoGebra 命令及参数

  1. Corner(1, 1) → G1Corner_1
  2. Corner(1, 2) → G1Corner_2
  3. Corner(1, 3) → G1Corner_3
  4. Corner(1, 4) → G1Corner_4
  5. Corner(2, 3) → G2Corner_3
  6. Corner(2, 4) → G2Corner_4
  7. Corner(2, 2) → G2Corner_2
  8. Corner(2, 1) → G2Corner_1
  9. CornerThreeD(-1, 1) → G3DCorner_1
  10. CornerThreeD(-1, 2) → G3DCorner_2
  11. CornerThreeD(-1, 3) → G3DCorner_3
  12. CornerThreeD(-1, 4) → G3DCorner_4
  13. CornerThreeD(-1, 5) → G3DCorner_5
  14. CornerThreeD(-1, 6) → G3DCorner_6
  15. CornerThreeD(-1, 7) → G3DCorner_7
  16. CornerThreeD(-1, 8) → G3DCorner_8
  17. Text("(c) Oliver Fechtig") → G2TextCopyrightDummy
  18. Corner(G2TextCopyrightDummy, 1) → G2TextCopyrightCorner_1
  19. Corner(G2TextCopyrightDummy, 2) → G2TextCopyrightCorner_2
  20. Corner(G2TextCopyrightDummy, 3) → G2TextCopyrightCorner_3
  21. Corner(G2TextCopyrightDummy, 4) → G2TextCopyrightCorner_4
  22. Textfield(time) → G2TimeIndex
  23. Text(G2TextCopyrightDummy) → G2TextCopyright
  24. Sequence(Circle[A_{3D} + (0, 0, (2 * s_1)), (c * (time - (k * T_1) - T_1 / 4)), Vector[(0, 0, 1)]], k, 0, 20) → Minima_{A,3D}
  25. Sequence(Circle[A_{3D} + (0, 0, (2 * s_1)), (c * (time - (((2 * k) + 1) / 2 * T_1) - T_1 / 4)), Vector[(0, 0, 1)]], k, 0, 20) → Maxima_{A,3D}
  26. Sequence(Circle[A_{2D}, (c * (time - (((2 * k) + 1) / 2 * T_1) - T_1 / 4))], k, 0, 20) → Maxima_{A,2D}
  27. Sequence(Circle[A_{2D}, (c * (time - (k * T_1) - T_1 / 4))], k, 0, 20) → Minima_{A,2D}
  28. Sequence(Circle[B_{2D}, (c * (time - (((2 * k) + 1) / 2 * T_2) - T_2 / 4)), xOyPlane], k, 0, 20) → Maxima_{B,2D}
  29. Sequence(Circle[B_{2D}, (c * (time - (k * T_2) - T_2 / 4)), xOyPlane], k, 0, 20) → Minima_{B,2D}
  30. Sequence(Circle[B_{3D} + (0, 0, (2 * s_2)), (c * (time - (k * T_2) - T_2 / 4)), Vector[(0, 0, 1)]], k, 0, 20) → Minima_{B,3D}
  31. Sequence(Circle[B_{3D} + (0, 0, (2 * s_2)), (c * (time - (((2 * k) + 1) / 2 * T_2) - T_2 / 4)), Vector[(0, 0, 1)]], k, 0, 20) → Maxima_{B,3D}