Uge 6 F13 Store Dag, opgave 6Fejl i facitlisten samt fejl i Maple-l\303\270sningen til l\303\246rerne!Generelt bevis for rotationsformel:http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotationshttp://mathworld.wolfram.com/RotationMatrix.htmlBegge kilder giver disse 3 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ser mystisk ud, at fortegnet p\303\245 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2KFEkc2luRicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lK2ZvcmVncm91bmRHUSxbMjU1LDAsMjU1XUYnLyUsbWF0aHZhcmlhbnRHUSVib2xkRicvJStmb250d2VpZ2h0R0Y6LUkobWZlbmNlZEdGJDYnLUYjNictRiw2KFEnJiM5NTI7RidGL0YyRjVGOEY7Ri9GNUY4RjtGL0Y1RjhGO0YvRjVGOEY7 er ombyttet ved rotation om y-aksen.Men det er korrekt!Bevis:Lad x-, y- og z-aksen er et s\303\246dvanligt h\303\270jreh\303\245ndssystem.I 2 dimensioner (planen) kender vi rotationsmatricen som: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LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIlPzhGKi0lLkJPVU5EU19IRUlHSFRHNiMkIiQhZkYqLSUpQ0hJTERSRU5HNiI=I 3 dimensioner (rummet) g\303\246lder s\303\245:Rotation om z-aksen: N\303\245r man sidder p\303\245 spidsen af z-aksen, og kikker ned, s\303\245 ligger x-aksen og y-aksen som vist.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LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIlZz1GKi0lLkJPVU5EU19IRUlHSFRHNiMkIiVdPUYqLSUpQ0hJTERSRU5HNiI=Situationen er som i 2D, dvs. x og y \303\246ndres som givet ved maticen: TUZOV3RLVWI8b2I8Uj1NRExDZE5iYlJRS2I6UmRjZEQ7XkFOXFxDX2I7X2RyT3VnaWVJP192d2VOdl1ZQV9DUWJMYGtPYWpeR2BDeXFPYF9iVlteZm5eRmNcXE5sYEdgZW5mW2dfRV5eUz9jTU9dU0djXFxgXmZeXFxEUXI8SF5DUWJCb1xcPk9sSmBcXF95eENpb1VZeXd4YEBZbXN3d1d5aFl2dm1AbWBpeXVYaEhpeVZZaUhJcW1xdm1xXltZeG1ZdD8/eWdBeUFnZTpfYE0+a2BPWkthY0pQW0NQdVdneXdpeV1Ybl1Qb1dYaXVXaV9obl9gdFlPaFxcQHFyQHlqQXhqeWl2cF5gbnF5eHFBV25zSXZbSVppaGl3Z2lEaW1TSXVTYXRVUHQ8eXdxeW1WYG1qaXM/aXI/WW9lWG9ZbmZtVl1FVl5dVl5OaWlIR2Jhd2ZhUGdcXHBzSHFzeGFjbWhfckhxc0h4c2Fpc0dpc3dmYXdmRVdjRU9sUmdcXERmanRPaXRvbFF4bGVXZ2VnZ3FnW2dhcHBwcFBobE9oYXZHYnlXZHlhdltBcWJAb2JPaGxPXFxLX3ZrSXhLZng7YF5AaGZfZ2Zfdl5hVmNcXFFleG9peE5zYF5wbWZhd2ZlWG9lSGBsZkFgVEh0S1ZgbVZgaHdwVXZ3a05lcW5gcF5ea15bTUB5c0l5U0FzTm9gRWlwaHBvaF5yPW5lQlZmcmBdWXZdaWhvZ0hhQHBmcD5yc3dkXFxeXVd3ZVl3eUhgb2NPbmVXX2VWX1h2a0FHcWFmYXdmaVtHZjtJYG52Y0dnY2NWW3VZa0VYW3M/aVR5dVl5YnRvcmVod2hodVdpdVtvYGVwbHk+dnhuc29XaG53bVtfaEhvY0hWdVZeXVZeZmtAa1dOcmBWcD1makBOZEt2YT5wZ1RJdVNJckpZZkVnQE1XW2lXXFxbd3ZfaXY/R21rRFBBd1NHZVNPdkVlR2dHZGpNZ3VXaVVTU0w9WUc/V0NTVHVLSXQ7WDxBdEpBRGV5WHZ3Q0FXcmVXZ2VfdVNlRkZdWEdDQ1hzZ2RXV01RdExBdE9xRk1hQ11XRVRLRXB1WHFFVXQ9Ym9pWG9lWEFzQkFbd0pbeUF1WGpzV0tZSWJrREh1U0lFaEN3eE1TRE1bd25rdFU/Z1RlZEdxQ0lzQ11leVBlVE9lcnBDVF4/ZmVNZ2VXZz9zU1NBY0BNck1dd0ZNU0RNdnNNeXBxeFBTZVppRF8/RGV5Qk5JUmJvWXFzSHFjaEdRZWJRdXFFZnhpd2dpc15NZTtdVndlWXdzRzs7SGpzZVhvZVJZeWBxdmBxbXdgWT5VdlZcXFNlbXZ2SXRLSWxMYVJmQHhqRFdOaHNcXGhtcHF4cG1ReUhUQE1WckBWdkRrXkhRdEhsZFBTVVRtWlxca3FZUkNFU0NheXZhWT5xVmdwWEdsVmJhUW1EVHk9dDpdazxFTEl5eGpJeEVRUk1VY1BmdnNBXW1Ydl1ZdmZYc3ZxaXluZjpnYj9nWmB3YVxcP2psTmY9PnFQdmpycV5gTmNkT2dkUGd3eF1BYXdGcGk8TnBUUGBGcXliX25EPm5Qd2tTbl50cFxca1llQl9jbWZtRWhhd2BgaXhvaVh2b1ZeXVZidT9bX2dpPlljeG5heD5gcj50VUBrWHFhWXhbRUZrZ2hvZ0hqO0haX3lkR15rSVByPFFieGdcXGBIXFxgP2o7b2tLQGRdeG09bm1OX2JAR2BMQXNKV2BFaWBwPl9rVnROV3lNT2RMX3NeSHFgcG5Adm9xeXhxUXU9b2VpeGR1WGxPTmBqblttZ11FdmJwaWlHVnlMdlo7eV1TbmNzT2BJPmpCVmdSXl1iZnZGYHhpVmNiSGBXT25BQXNyaGtrVnNvXnRZT288WFtLUVpjX3RGaVpPPls9P3I7P3VLZ2RhYG9qRmJbSGBxdmBhYGE+UHlNZl1BcXZ0QXVSQV1pX1pbcG1RUHBEcWVaP2JXV2pUcGBcXGd0ZEdfXFxYXWM/bFpXcFZXWl1Ab1teZEVfb2BwbmBWbFFpc2JeYEpuaHJPdT1Bb2FpaEQ/YFJecjxGbE9meWZPaFpfdWtJYDtYYkRhXWlQbXdBZVhIcHBGbEtGbDtgd3RoZkxmdUJBeVJ3YFFpYD5PWmpRc3V5XWdPbndnbVNoXkBQY1VmX1xcZ2A/YHBBYHJQP2RKP2pJYHZjaVtfZ2JQb2RQTmZXVmVMd2VWX2VqaHROVmFEUF52WG9lWFtFT2RwYG5QZ2o+XmtYbnFQdmtvPnVUQGtCcGJcXF9xXFx2Y11uYGxYXXg+bXQ+ZV1GZk1uYG1YYUFma0doa0J3dlJZak9XZFo+XFxKZ2h0SHFoSG55RmRxPm47b2llUXZ2YXlWd3ZvSFtUeWVwT3JVP2lfYHFjZmNqb1xcbmBbTHlrPnB5Pj5rYE9uU0BiblY8R21iP15USFs+V2A7QGdgPlxcR2FCPT5MSkthU1pCaz9IQUVEY11VcDtHYV9FTG1IUVtXUF1SVFtkR0tTZXNiTmdzP1NIT0NkY3lVQkd3XWlDRHFCX2dkPU1TX1FieGVSXm9kO0FDblNoOj9GZldieEViVktURldDdGlES09VQGNzQ0t1QF1WPU9IRUlGX09YO11lXFxLdG5FdVo/VnNbZm1lRFdPdk5DZFA9c0BjUkRJRldjZ2JhRGE/Y25PUnA7R0xtQ3NZeU5jZWBZR1xcY1VQQXNAY2dKV1J4dURuYUVeP3dOUXJaT0Zsa2hMW0NrXUNNS0JdeUhKO2thUVFZeFdMZE5FPHFuTG07XVNmVE9AbFlWUWtIQXdYVUttRVJKUE5MaVZTYFdKYVVzXFx2cT1YSlBubVlRQkBUPk1xZjxsR0xrTl55P05rSEdiREBjUWhabEhiS1BoQnduZU5hP0ZfXFxmZVA+c0BmYkRJXldwb2JhYFNHXFxTR2VTR3F3aHFHd3k7SHZWP2dTXmtKXnBtV2htR2xlQG9tYG1FZl89YHhtUGp5RlpcXEhtYm9eSjpMXUI8WkthY1o6PVhEW0d2V0RPc2hoV1NMO1NldUltW0dcXHllYj91alNlXXF0b0VTPENJZ3lVVVVVPUdWZHdJbmVoR29WXXN5bnVGPVtGbndFTT9FPWVHUltDZGF5b3NmQktlR195TWllRjtkSnFZcVd1dz1Yaj1iVklEQXlZY1VVP1VoS2NVUV9Dak1pd1FGYm15SHV0b1F5dFF3Tk92RUl0cFlDXFxHdVpvZ0VxWHJjdXhVSVFpc3RpWFdNWDxJdHBZVTxVaDtlVVFnd2pNaXdRYmJtSGJXd2xnRUh1aFldVUpxSFxcV3dMR0JIdXBaTG1HQHd0YGZhWHVpaktkVVFgS0pgdXhdalBAbUh5cGRxdD9ITFd1bF5Ed1NNUnVZTVVUTWl0T2l0S0l0S1d1VUlYWGtBWXZMc0FFdlJBUm1Yd0VVeVVUdFddTFNBTltoeWt1dV9UbnVpc3lNSj5VUEtbVl5qQmleUnlyQXlqZEldVGZnZ2dnUGZhc2ZqWl9dW0BkQkd5SmBuaj9hZnhwTHFbPk5aRGljaXh0RV9gRWFxRHlkd3ZbUGd4blBqPk5pQEFbX3FmPEZUWjtfYHhZWl1GYUZhaUZZXmdgTT5aQ2diSF9iaFBiWk82SlwiXHtcfQ==LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIlITQlISIiLSUpQk9VTkRTX1lHNiMkIiIhRiotJS1CT1VORFNfV0lEVEhHNiMkIiU/O0YqLSUuQk9VTkRTX0hFSUdIVEc2IyQiJEkqRiotJSlDSElMRFJFTkc2Ig==Rotation om x-aksen: N\303\245r man sidder p\303\245 spidsen af x-aksen, og kikker ned, s\303\245 ligger y-aksen og z-aksen som vist.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Situationen er som i 2D, dvs. y og z \303\246ndres som givet ved maticen: 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LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIlITMlISIiLSUpQk9VTkRTX1lHNiMkIiIhRiotJS1CT1VORFNfV0lEVEhHNiMkIiUrO0YqLSUuQk9VTkRTX0hFSUdIVEc2IyQiJD8qRiotJSlDSElMRFJFTkc2Ig==Rotation om y-aksen: N\303\245r man sidder p\303\245 spidsen af y-aksen, og kikker ned, s\303\245 ligger x-aksen og z-aksen som vist.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LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIlUz5GKi0lLkJPVU5EU19IRUlHSFRHNiMkIiUrPkYqLSUpQ0hJTERSRU5HNiI=Enhedsvektoren 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 , som p\303\245 figuren g\303\245r lodret opad, drejes over i enhedsvektoren 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, n\303\245r man drejer \316\270 grader imod uret om y-aksen (bem\303\246rk at z bliver negativ).Enhedsvektoren 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 , drejes over i sig selv, dvs. 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, som p\303\245 figuren g\303\245r vandret til h\303\270jre, drejes over i enhedsvektoren 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n\303\245r man drejer \316\270 grader imod uret om y-aksen.Derfor bliver rotationsmatricen om y-aksen: 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angivet p\303\245 Wikipedia og p\303\245 Wolfram!Svar p\303\245 opgave 6, 1. sp\303\270rgsm\303\245l:Bem\303\246rk at der roteres om y-aksen, vinklen er 45\302\260, og retningen er med uret.Dvs. 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l\303\246gges parallelforskydningen p\303\245 (1,0,1).LCZJIiVHNiIiIiItSSQ8LD5HSShfc3lzbGliR0YkNiVGJSIiIUYlRiU=Konklusion:Efter rotationen er parameterfremstillingen 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n\303\245r man regner i 3D.TTdSMApJN1JUQUJMRV9TQVZFLzQ1NzQ5MjQyMjZYLCUpYW55dGhpbmdHNiJGJVtnbCEiJSEhISMqIiQiJC1JJGNvc0c2JCUqcHJvdGVjdGVkRyUoX3N5c2xpYkc2IywkJSNQaUcjISIiIiIlIiIhLCQtSSRzaW5HNiRGKUYqRitGL0YxIiIiRjFGM0YxRiZGJQ==TTdSMApJN1JUQUJMRV9TQVZFLzQ1NzQ5MjQ2MTBYKiUpYW55dGhpbmdHNiJGJVtnbCEjJSEhISIkIiQlInVHIiIhKiRGJiIiI0YlTTdSMApJN1JUQUJMRV9TQVZFLzQ1ODU5MzA3NTRYKiUpYW55dGhpbmdHNiJGJVtnbCEjJSEhISIkIiQsJiomIiIjIyIiIkYoJSJ1R0YqRikqJkYoRilGK0YoIyEiIkYoIiIhLCZGJ0YpRixGKUYlTTdSMApJN1JUQUJMRV9TQVZFLzQ1ODU5MzEyNjZYKiUpYW55dGhpbmdHNiJGJVtnbCEjJSEhISIkIiQsKComIiIjIyIiIkYoJSJ1R0YqRikqJkYoRilGK0YoIyEiIkYoRipGKiIiISwoRidGKUYsRilGKkYqRiU=