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平面薄板质心计算入门

平面薄板质心计算入门
几何画板及绘图内容加载中，请稍等……
2021-08-19 00:53
多边形向量解析几何微积分积分
本范例演示如何通过积分计算平面薄板的质心。涉及的核心数学概念包括积分计算、向量运算和多边形处理。作图要点包括使用FitPoly拟合多边形边界，通过Integral计算面积和质心坐标，以及利用Sequence和Polygon构建图形。适合高中及以上学生学习和理解质心计算方法。

GeoGebra 命令及参数

  1. FitPoly(l1, 3) → f
  2. Integral(f, 1, 9) → a
  3. Sequence((1 + ((k - 1) * d), 0), k, 1, n + 1) → l3, {(1, 0), (1.8, 0), (2.6, 0), (3.4000000000000004, 0), (4.2, 0), (5, 0), (5.800000000000001, 0), (6.6000000000000005, 0), (7.4, 0), (8.2, 0), (9, 0)}
  4. Sequence((b + ((k - 1) * d), f(b + ((k - 1) * d))), k, 1, n + 1) → l2, {(1.4, 3.4118779378900292), (2.2, 3.445108344369352), (3, 3.4004365133494336), (3.8000000000000003, 3.324094732171628), (4.6, 3.2623152881772897), (5.4, 3.261330468707774), (6.200000000000001, 3.367372561104435), (7, 3.6266738527086266), (7.800000000000001, 4.085466630861706), (8.6, 4.78998318290502), (9.4, 5.7864557961799346)}
  5. Sequence((x(l3(2)) + ((k - 1) * d), f(b + ((k - 1) * d))), k, 1, n) → l5, {(1.8, 3.4118779378900292), (2.6, 3.445108344369352), (3.4000000000000004, 3.4004365133494336), (4.2, 3.324094732171628), (5, 3.2623152881772897), (5.8, 3.261330468707774), (6.6000000000000005, 3.367372561104435), (7.4, 3.6266738527086266), (8.200000000000001, 4.085466630861706), (9, 4.78998318290502)}
  6. Sequence((1 + ((k - 1) * d), f(b + ((k - 1) * d))), k, 1, n) → l4, {(1, 3.4118779378900292), (1.8, 3.445108344369352), (2.6, 3.4004365133494336), (3.4000000000000004, 3.324094732171628), (4.2, 3.2623152881772897), (5, 3.261330468707774), (5.800000000000001, 3.367372561104435), (6.6000000000000005, 3.6266738527086266), (7.4, 4.085466630861706), (8.2, 4.78998318290502)}
  7. Sequence(Polygon[(1 + ((k - 1) * d), 0), (x(l5(1)) + ((k - 1) * d), 0), (x(l5(1)) + ((k - 1) * d), f(b + ((k - 1) * d))), (1 + ((k - 1) * d), f(b + ((k - 1) * d)))], k, 1, n) → l6, {2.729502350312024, 2.7560866754954816, 2.7203492106795473, 2.659275785737301, 2.609852230541832, 2.6090643749662163, 2.693898048883547, 2.9013390821669027, 3.2683733046893693, 3.8319865463240177}
  8. Polygon(N, O, Q, P) → q1, n_1, o, q, p
  9. Point(xAxis) → R
  10. Segment(R, S) → h
  11. Point(xAxis) → T
  12. Segment(T, U) → i
  13. Vector(W, V) → u
  14. Vector(A_1, Z) → v
  15. Midpoint(V, Z) → B_1
  16. Vector(C_1, D_1) → w
  17. Vector(D_1, C_1) → j
  18. Midpoint(C_1, D_1) → E_1
  19. Vector(F_1, H_1) → k
  20. Vector(H_1, F_1) → l
  21. Midpoint(F_1, H_1) → I_1

AI 绘图提示语参考

描述一个平面 lamina 的质心计算示意图。图中包含一个多边形区域，代表 lamina 的形状；一些点表示质心坐标；线段和向量表示积分计算和向量运算过程。整体展示质心计算方法，适用于学习积分与向量运算的学生。
以上提示语为根据原始绘图命令整理而来，仅供参考。