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刚体旋转

刚体旋转
几何画板及绘图内容加载中，请稍等……
2016-04-28 07:56
向量矩阵
该范例演示了刚体旋转的几何现象。核心数学概念包括旋转矩阵和向量。通过使用GeoGebra命令如Sequence、Circle、Line等，可以动态展示刚体旋转过程中的几何变换。适合高中及以上学生学习几何变换和向量知识。

GeoGebra 命令及参数

  1. Sequence(Sequence[Vector[(j, k), (j + (scale * F_1(j, k)), k + (scale * F_2(j, k)))], j, xmin, xmax, xstep], k, ymin, ymax, ystep) → vField
  2. Sequence(((x(Element[inicialPts, i]) * cos((w * time))) - (y(Element[inicialPts, i]) * sin((w * time))), (x(Element[inicialPts, i]) * sin((w * time))) + (y(Element[inicialPts, i]) * cos((w * time)))), i, 1, 8) → particlesList
  3. Sequence(CurveCartesian[(x(Element[inicialPts, i]) * cos((w * t))) - (y(Element[inicialPts, i]) * sin((w * t))), (x(Element[inicialPts, i]) * sin((w * t))) + (y(Element[inicialPts, i]) * cos((w * t))), t, 0, time], i, 1, 8) → pathlinesList
  4. Sequence(Vector[Element[particlesList, i], (x(Element[particlesList, i]) + (scale * F_1(x(Element[particlesList, i]), y(Element[particlesList, i]))), y(Element[particlesList, i]) + (scale * F_2(x(Element[particlesList, i]), y(Element[particlesList, i]))))], i, 1, 8) → vectorParticles
  5. Sequence(Segment[Rotate[curlPt - (0.6, 0), k + curlAngle, curlPt], Rotate[curlPt + (0.6, 0), k + curlAngle, curlPt]], k, 0, 2.0944, 1.0472) → spokes
  6. Circle(divPt, 0.6) → divGlowCircle
  7. Line(I, xAxis) → f
  8. Line(J, xAxis) → g
  9. Line(K, xAxis) → h