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拉格朗日点V1.1

拉格朗日点V1.1
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2019-05-14 12:21
解析几何变换几何作图
该范例演示了拉格朗日点的几何构造。涉及的核心数学概念包括几何变换和轨迹。通过使用Circle, Point, Rotate, Line, Segment等GeoGebra命令，可以构造出地球和太阳之间的拉格朗日点L1至L5。适合高中及以上学生或教师使用。

GeoGebra 命令及参数

  1. Circle(Origin, 3.14) → orbit
  2. Point(orbit) → Earth_{01}
  3. Rotate(Earth_{01}, angle_{01} + 64°, Origin) → L_{4}
  4. Rotate(Earth_{01}, angle_{01} + 180°, Origin) → L_{3}
  5. Rotate(Earth_{01}, angle_{01} + 296°, Origin) → L_{5}
  6. Rotate(Earth_{01}, angle_{01}, Origin) → Earth_{02}
  7. Line(Origin, Earth_{02}) → f
  8. Point(f) → L_{2}
  9. Point(f) → L_{1}
  10. Segment(Origin, L_{4}) → g
  11. Segment(Origin, L_{3}) → h
  12. Segment(Origin, L_{5}) → i
  13. Segment(Origin, Earth_{02}) → j
  14. Circle(Origin, L_{1}) → Circle_{L1}
  15. Circle(Origin, L_{2}) → Circle_{L2}
  16. Rotate(L_{1}, angle_{01}, Origin) → L1_B
  17. Rotate(L_{2}, angle_{01}, Origin) → L2_B