• 2022-11-03
    证明绕原点的全体旋转变换构成群。
  • 证: 设 [tex=11.0x3.357]hIMQ9Mbwf2StKNAONM7LIEQXexHv8e9JsWjTrJq/AJBzgGg72mhAbC3A9XZz5I76ou+G1pgs8DrThGF7qrFp6aj3ZFvp/AdK16E+FkxFf6KOCtqMdklfNevXA3eJfqurOsi+R+J/stWaSxuxNrTW5ehsf6JTrSeAtGRKhKqyxwMFGVh3klOxRjMXGFaGeu88[/tex]且 [tex=10.643x2.786]d4rZktZRCtsvPHN2eZ3+yxem0Qf84B4m4xTyqFQx5PbjWwJb21do6IKTZAAXEf+dkwLuWT19rDfRlSosj9zNHHfeT0dVemsRYSXpEv/8j05bs9pR+YBSg9vfOtf/SBAVQdC8lwakDkHYoVS36BxD5g==[/tex][tex=12.5x3.357]YRUOTNKyUq6sYrKuivudXrk4l4uUSDcGFw8vU7dWQ8IRn2Q8oX49LIqQI5pfR4IdlF6X7jJBkVljHyk6WbEMxpBVgFM4hWo2HuBT+e1VBkyuXXmowbIWdlv4t2EaFr6E7hWhVmVLt/JcSd8WauyUVgQO5GkRhuT/KHeAaNO4Sfu3duB76/EhJVgOc+6dtcegcg7ZvvbXA26SEhGAw2/CkyPRXbXhkkf1Aw4bm1bZ3Wh8tOp/aXP+A1gpuqF3TUdkNHcPJsxttIWCpL73kM+3rw5uKcppBpqeDO7idqQBq/o=[/tex]且 [tex=11.357x2.786]g/6lRpUjbtBCjDcVWBWnXoRSmTPfpe3xDcy8j2QhtrJbvCWiPNJ50+vDRgyVWO14PE/OnIJQ07I5v6N+NAfa+tb0wQYpqdegCmzM5LAXjQTEeXxy0Q372+IeJ9eZlxqUcUvtoqj9oK8VfYKVQMh0i+sHQGOcRMvH86LpVA2/KoeNpJOaaFtQkX0uFvF2gmnKgAYrf198KKvFG0TrIiKjog==[/tex]所以 [tex=17.643x3.357]Gatld9Xckov7GQ8RMgGeooNKRNzzaE/aVetOR0IgtB2ftpJpj1hDI+L6ioKNMHTJ+2vDxB1/kZGUx+k4ACMzKzKQC36/UsZiO5t2AEsvLt4olEN/SkOaNTOo5bKqeJZWKxVnZotMh03DpmCh/YL5qTcGZCABuNRViHIlrYehUZqH3x1On/mqJFyR0POnFehmHgLh2wr6JIy3E8hU4hwhLEzTyiwlChoMjYOPWgsX0NtsJ12y8luLx2POCZF53hKU+eCYaI73zbgGDA8vt0DJnwKhhRGnWVjGzqAVQw7BQDaa2U+tC3JbCwEZt+s5eK/KTegdFkWi7DACM2f0x/0XqFOVLug8Byxh9AziNsES1dn6KOE/FZqz9c97jhbArPh3[/tex]且 [tex=15.286x3.357]rD0fTcokqUjPlLOdGMIUmwL7/x1IPEVrtMf5CGSibeIFzPNPkO0aV9CUhbEnbs6YrRewaY0GYmq6mQizjegT7eNgGrKopB+EYO/T3XIsYLqJw5uzNFTjexf8K1KRXENM1im6nXSHYvFtqBMFU5psGFC/SMycur1Q0/ZQhmfuuFHplJV16SCppgK6G+TMm+QJJQ+a8JFFbabeMn60QX+UtX3ZqkdkGzOEcxFtDVyunyvRYyr8qbRbX5jhrJpOkgYq+AjYlrCJlNQ+RtVhZDXgylyl3dozXNTzFEt+OoXlP+s=[/tex]故旋转变换之积仍为旋转变换;又因为 [tex=15.929x3.357]jpKHmouLwV27Z9zFqlxLiYhtiVSC9CpyXFtyK9tZmLCwqgnAjMfh/7jAx4EXabOfmr8nBRXBhO4k9DVu78fJDJc+8J46LdghrI5GN44khT/igPRiQGLTLz3UaWmg1Ijl7GzfqpsSFxlypPNO5yve2kOGPGkxFMJ9KXZ7R2s4Zt1UWSU4KjeswztvYK4DHhgFubCUjK/u+KxMBRKue9IAR18CysfnHNNzgLdu50Xi/f/jUsMUI3scpyJzJIqhpzZo[/tex][tex=10.357x3.357]7EJHVCtO2IWq3KpdB+jQsqRoX5mLP4++02LSSQDOWULAeUAPaYFDhYBHAfNRE+KFavwMWms6ZRQlkBYdwSdjY4MR5PL+0iEhMNltFgano9PzwJBEZUUKao8e0V81PJ7IQdMI8xQreyfc+dy1/hWOI8igkZbeb0m7Nk7vw3rqyrF4fvi3WtDbWSVd3eESVftd[/tex]其 [tex=11.571x2.786]3oMu+M3Y0Pg3/Ytqj7flKyG3MI6vREy+b4TqJFV1M8QZYktolFXMxlfyzjanoBPA85HnIza3kf65U2ptHtQDYOaMDOyjkRB0Kd3mSfLohdI2qI4hzXJ34OVDffZVkC/uzkHARqERhexs3BgWj/5IZQ==[/tex],故旋转变换之逆仍为旋转变换,所以绕原点的旋转变换构成群。

    内容

    • 0

      手臂绕定轴转动是相对固定坐标系作旋转变换,手部绕手腕轴旋转是相对动坐标系作旋转变换。

    • 1

      三维旋转变换是指绕坐标轴的旋转

    • 2

      三维旋转变换可以绕空间一个点变换。()

    • 3

      4. 三维基本旋转变换是指下列哪些? A: 绕x轴旋转 B: 绕y轴旋转 C: 绕z轴旋转 D: 绕任意轴旋转

    • 4

      使用下列二维图形变换矩阵: 产生变换的结果为() A: 沿X坐标轴平移1个绘图单位,同时,沿Y坐标轴平移-1个绘图单位 B: 绕原点逆时针旋转90度 C: 沿X坐标轴平移-1个绘图单位,同时,沿Y坐标轴平移1个绘图单位 D: 绕原点顺时针旋转90度