水波模拟

水波模拟
几何画板及绘图内容加载中,请稍等……
2016-05-16 01:29
该范例演示了水波的波动现象。涉及的核心数学概念包括三角函数和参数方程。通过使用GeoGebra命令如CurveCartesian、Line、Sequence等,可以构造出波动图形。适合高中及以上学生学习波动原理和参数方程。

GeoGebra 命令及参数

  1. CurveCartesian(0, k, f(k), k, 0, 100) → b
  2. Line((0, 0), k) → c
  3. Sequence(Rotate[b, α, c], α, 0, 6.283185307179586, 0.1) → llista1, {(0, k, (2 * cos((0.5 * k) - (3 * 0)))), ((0.9950041652780257 * 0) + (-0.09983341664682815 * k), (0.09983341664682815 * 0) + (0.9950041652780257 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((0.9800665778412416 * 0) + (-0.19866933079506122 * k), (0.19866933079506122 * 0) + (0.9800665778412416 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((0.955336489125606 * 0) + (-0.2955202066613396 * k), (0.2955202066613396 * 0) + (0.955336489125606 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((0.9210609940028851 * 0) + (-0.3894183423086505 * k), (0.3894183423086505 * 0) + (0.9210609940028851 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((0.8775825618903728 * 0) + (-0.479425538604203 * k), (0.479425538604203 * 0) + (0.8775825618903728 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((0.8253356149096783 * 0) + (-0.5646424733950354 * k), (0.5646424733950354 * 0) + (0.8253356149096783 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((0.7648421872844885 * 0) + (-0.644217687237691 * k), (0.644217687237691 * 0) + (0.7648421872844885 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((0.6967067093471655 * 0) + (-0.7173560908995227 * k), (0.7173560908995227 * 0) + (0.6967067093471655 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((0.6216099682706646 * 0) + (-0.7833269096274833 * k), (0.7833269096274833 * 0) + (0.6216099682706646 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((0.5403023058681398 * 0) + (-0.8414709848078965 * k), (0.8414709848078965 * 0) + (0.5403023058681398 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((0.4535961214255773 * 0) + (-0.8912073600614354 * k), (0.8912073600614354 * 0) + (0.4535961214255773 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((0.3623577544766734 * 0) + (-0.9320390859672264 * k), (0.9320390859672264 * 0) + (0.3623577544766734 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((0.2674988286245871 * 0) + (-0.9635581854171931 * k), (0.9635581854171931 * 0) + (0.2674988286245871 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((0.1699671429002406 * 0) + (-0.9854497299884603 * k), (0.9854497299884603 * 0) + (0.1699671429002406 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((0.07073720166770246 * 0) + (-0.9974949866040544 * k), (0.9974949866040544 * 0) + (0.07073720166770246 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((-0.029199522301289256 * 0) + (-0.9995736030415051 * k), (0.9995736030415051 * 0) + (-0.029199522301289256 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((-0.1288444942955253 * 0) + (-0.9916648104524686 * k), (0.9916648104524686 * 0) + (-0.1288444942955253 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((-0.22720209469308775 * 0) + (-0.973847630878195 * k), (0.973847630878195 * 0) + (-0.22720209469308775 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((-0.3232895668635042 * 0) + (-0.9463000876874142 * k), (0.9463000876874142 * 0) + (-0.3232895668635042 * k), (0.9999999999999999 * (2 * cos((0.5 * k) - (3 * 0))))), ((-0.4161468365471424 * 0) + (-0.9092974268256817 * k), (0.9092974268256817 * 0) + (-0.4161468365471424 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((-0.5048461045998575 * 0) + (-0.8632093666488738 * k), (0.8632093666488738 * 0) + (-0.5048461045998575 * k), (0.9999999999999999 * (2 * cos((0.5 * k) - (3 * 0))))), ((-0.5885011172553458 * 0) + (-0.8084964038195901 * k), (0.8084964038195901 * 0) + (-0.5885011172553458 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((-0.6662760212798243 * 0) + (-0.74570521217672 * k), (0.74570521217672 * 0) + (-0.6662760212798243 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((-0.7373937155412458 * 0) + (-0.6754631805511506 * k), (0.6754631805511506 * 0) + (-0.7373937155412458 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((-0.801143615546934 * 0) + (-0.5984721441039561 * k), (0.5984721441039561 * 0) + (-0.801143615546934 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((-0.8568887533689475 * 0) + (-0.5155013718214637 * k), (0.5155013718214637 * 0) + (-0.8568887533689475 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((-0.9040721420170614 * 0) + (-0.42737988023382933 * k), (0.42737988023382933 * 0) + (-0.9040721420170614 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((-0.9422223406686584 * 0) + (-0.3349881501559042 * k), (0.3349881501559042 * 0) + (-0.9422223406686584 * k), (0.9999999999999999 * (2 * cos((0.5 * k) - (3 * 0))))), ((-0.9709581651495908 * 0) + (-0.23924932921398154 * k), (0.23924932921398154 * 0) + (-0.9709581651495908 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((-0.9899924966004454 * 0) + (-0.1411200080598672 * k), (0.1411200080598672 * 0) + (-0.9899924966004454 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((-0.9991351502732795 * 0) + (-0.04158066243329049 * k), (0.04158066243329049 * 0) + (-0.9991351502732795 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((-0.9982947757947531 * 0) + (0.058374143427580086 * k), (-0.058374143427580086 * 0) + (-0.9982947757947531 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((-0.9874797699088649 * 0) + (0.15774569414324865 * k), (-0.15774569414324865 * 0) + (-0.9874797699088649 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((-0.9667981925794609 * 0) + (0.25554110202683167 * k), (-0.25554110202683167 * 0) + (-0.9667981925794609 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((-0.9364566872907962 * 0) + (0.3507832276896203 * k), (-0.3507832276896203 * 0) + (-0.9364566872907962 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((-0.8967584163341468 * 0) + (0.44252044329485285 * k), (-0.44252044329485285 * 0) + (-0.8967584163341468 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((-0.8481000317104078 * 0) + (0.5298361409084937 * k), (-0.5298361409084937 * 0) + (-0.8481000317104078 * k), (0.9999999999999999 * (2 * cos((0.5 * k) - (3 * 0))))), ((-0.7909677119144163 * 0) + (0.6118578909427197 * k), (-0.6118578909427197 * 0) + (-0.7909677119144163 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((-0.7259323042001395 * 0) + (0.6877661591839744 * k), (-0.6877661591839744 * 0) + (-0.7259323042001395 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((-0.6536436208636119 * 0) + (0.7568024953079282 * k), (-0.7568024953079282 * 0) + (-0.6536436208636119 * k), (0.9999999999999999 * (2 * cos((0.5 * k) - (3 * 0))))), ((-0.5748239465332692 * 0) + (0.8182771110644103 * k), (-0.8182771110644103 * 0) + (-0.5748239465332692 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((-0.49026082134070026 * 0) + (0.8715757724135877 * k), (-0.8715757724135877 * 0) + (-0.49026082134070026 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((-0.4007991720799763 * 0) + (0.9161659367494546 * k), (-0.9161659367494546 * 0) + (-0.4007991720799763 * k), (0.9999999999999999 * (2 * cos((0.5 * k) - (3 * 0))))), ((-0.307332869978421 * 0) + (0.9516020738895156 * k), (-0.9516020738895156 * 0) + (-0.307332869978421 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((-0.21079579943078144 * 0) + (0.9775301176650967 * k), (-0.9775301176650967 * 0) + (-0.21079579943078144 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((-0.11215252693505663 * 0) + (0.9936910036334642 * k), (-0.9936910036334642 * 0) + (-0.11215252693505663 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((-0.012388663462893225 * 0) + (0.9999232575641008 * k), (-0.9999232575641008 * 0) + (-0.012388663462893225 * k), (0.9999999999999999 * (2 * cos((0.5 * k) - (3 * 0))))), ((0.08749898343944375 * 0) + (0.9961646088358409 * k), (-0.9961646088358409 * 0) + (0.08749898343944375 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((0.18651236942257227 * 0) + (0.9824526126243331 * k), (-0.9824526126243331 * 0) + (0.18651236942257227 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((0.2836621854632263 * 0) + (0.9589242746631385 * k), (-0.9589242746631385 * 0) + (0.2836621854632263 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((0.37797774271298024 * 0) + (0.9258146823277325 * k), (-0.9258146823277325 * 0) + (0.37797774271298024 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((0.46851667130037633 * 0) + (0.8834546557201536 * k), (-0.8834546557201536 * 0) + (0.46851667130037633 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((0.55437433617916 * 0) + (0.8322674422239018 * k), (-0.8322674422239018 * 0) + (0.55437433617916 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((0.6346928759426332 * 0) + (0.7727644875559883 * k), (-0.7727644875559883 * 0) + (0.6346928759426332 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((0.7086697742912588 * 0) + (0.7055403255703931 * k), (-0.7055403255703931 * 0) + (0.7086697742912588 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((0.7755658785102485 * 0) + (0.631266637872323 * k), (-0.631266637872323 * 0) + (0.7755658785102485 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((0.8347127848391583 * 0) + (0.5506855425976398 * k), (-0.5506855425976398 * 0) + (0.8347127848391583 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((0.8855195169413177 * 0) + (0.4646021794137597 * k), (-0.4646021794137597 * 0) + (0.8855195169413177 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((0.9274784307440346 * 0) + (0.3738766648302393 * k), (-0.3738766648302393 * 0) + (0.9274784307440346 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((0.9601702866503661 * 0) + (0.27941549819892586 * k), (-0.27941549819892586 * 0) + (0.9601702866503661 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((0.9832684384425845 * 0) + (0.1821625042720959 * k), (-0.1821625042720959 * 0) + (0.9832684384425845 * k), (2 * cos((0.5 * k) - (3 * 0)))), ((0.9965420970232174 * 0) + (0.08308940281749728 * k), (-0.08308940281749728 * 0) + (0.9965420970232174 * k), (2 * cos((0.5 * k) - (3 * 0))))}
  4. Textfield(k_x) → CampEntradaSortida1
  5. Textfield(ω) → CampEntradaSortida2
  6. Textfield(A) → CampEntradaSortida3
  7. Segment((0, 0, A), (0, 0, (-A))) → d
  8. Surface((u * cos(v)), (u * sin(v)), f(u), u, 0, 100, v, 0, 6.285) → e

AI 绘图提示语参考

画一个水波纹模拟图,展示波浪运动。主要包含一个正弦波形曲线,以及多条围绕该曲线旋转并缩小的副本,形成层叠的波浪效果。先画出中心的主波形,然后围绕它生成多条旋转的波形,最后添加一个垂直线段作为参考。
以上提示语为根据原始绘图命令整理而来,仅供参考。