空间曲线及其方程

空间曲线及其方程 JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK 1lÙ m)ÛAÛþê § 8.4 m9Ù§ �+ ênÆ� �®nóÆ¾°Æ� School of Science Zhuhai Campus of Beijing Institute of Technology YUAN Peng SS, at ZHBIT 111lllÙÙÙ ...

JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK 1lÙ m)ÛAÛþê § 8.4 m9Ù§ �+ ênÆ� �®nóÆ¾°Æ� School of Science Zhuhai Campus of Beijing Institute of Technology YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK Jj 1 m�§ 2 m�ëê§ 3 m3I¡þ�ÝK YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK µe 1 m�§ 2 m�ëê§ 3 m3I¡þ�ÝK YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK m�§ mCwmü¡� �. { F(x, y, z) = 0, G(x, y, z) = 0 mmm��§§§AAA:::µµµ þ�:Ñ÷v§§÷v§ �:Ñ3þ§Ø3þ� :ØUÓ÷vü§. m YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK m�§ ~1 §|{ x2 + y2 = 1, 2x + 3z = 6 L«N��º ) §x2 + y2 = 1L«1²1uz¶��Î¡§Ù O´xOy¡þ��§�%3O ,»1¶ §2x + 3z = 6L«1²1uy¶�Î¡§ du§�O´zOx¡þ�§Ïd§´² ¡" §|ÒL«þã²¡�Î¡��" YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK m�§ ~2 §| z = √ a2 − x2 − y2,( x − a 2 )2 + y2 = (a 2 )2 L«N��º ) 1§L«¥%3O ,»a�þ¥¡¶ 1�§L«1²1uz¶��Î¡§§�O ´xOy¡þ��" §|ÒL«þã¥¡�Î¡��" YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK m�§ ~2 §| z = √ a2 − x2 − y2,( x − a 2 )2 + y2 = (a 2 )2 L«N��º ) 1§L«¥%3O ,»a�þ¥¡¶ 1�§L«1²1uz¶��Î¡§§�O ´xOy¡þ��" §|ÒL«þã¥¡�Î¡��" YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK µe 1 m�§ 2 m�ëê§ 3 m3I¡þ�ÝK YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK m�ëê§ mmmC��ëëëêêê§§§µµµ x = x(t), y = y(t), z = z(t). �½t = t1§Ò��Cþ�:(x1, y1, z1)§X ëêt�Cz��Cþ��Ü:. YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK m�ëê§ mmmC��ëëëêêê§§§µµµ x = x(t), y = y(t), z = z(t). �½t = t1§Ò��Cþ�:(x1, y1, z1)§X ëêt�Cz��Cþ��Ü:. YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK m�ëê§ ~2 XJm:M3�Î¡ x2 + y2 = a2 þ±�Ýω7z¶^=§Ó q±Ýv÷²1uz¶�� þ,£Ù¥ω!vÑ´~ ê¤§@o:M�¤�ã/� ÚÚÚ^^^©ÁïáÙëê§© YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK m�ëê§ ) �mtëê" ��t = 0§Ä: ux¶þ� :A(a, 0, 0)?" ² L mt§ Ä : dA$ Ä �M(x, y, z)" PM3¡xOyþ�ÝKM ′ § KM ′ �I(x, y, 0)" YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK m�ëê§ ) duÄ:3�Î¡þ±� Ýω7¶z^=§¤±²L mt§∠AOM ′ = ωt"l x = |OM′ | cos ∠AOM′ = a cosωt y = |OM′ | sin ∠AOM′ = a sinωt duÄ:Ó±Ýv÷²1 uz¶��þ,§¤± z = M ′ M = vt YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK m�ëê§ ) ÏdÚ^�ëê§ x = a cosωt , y = a sinωt , z = vt . YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK m�ëê§ Ú^ YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK µe 1 m�§ 2 m�ëê§ 3 m3I¡þ�ÝK YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK m3I¡þ�ÝK §H(x, y) = 0L« 1²1uz¶§OxOy¡ þ�H(x, y) = 0�Î¡§Î¡¹ Tm" ¡Î¡H(x, y) = 0m'uxOy¡�ÝKÎ¡" ÝÝÝKKKÎÎÎ¡¡¡��AAA��µµµ ±dmO§Ru¤ÝK�I¡. YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK m3I¡þ�ÝK §H(x, y) = 0L« 1²1uz¶§OxOy¡ þ�H(x, y) = 0�Î¡§Î¡¹ Tm" ¡Î¡H(x, y) = 0m'uxOy¡�ÝKÎ¡" ÝÝÝKKKÎÎÎ¡¡¡��AAA��µµµ ±dmO§Ru¤ÝK�I¡. YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK m3I¡þ�ÝK §H(x, y) = 0L« 1²1uz¶§OxOy¡ þ�H(x, y) = 0�Î¡§Î¡¹ Tm" ¡Î¡H(x, y) = 0m'uxOy¡�ÝKÎ¡" ÝÝÝKKKÎÎÎ¡¡¡��AAA��µµµ ±dmO§Ru¤ÝK�I¡. YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK m3I¡þ�ÝK §H(x, y) = 0L« 1²1uz¶§OxOy¡ þ�H(x, y) = 0�Î¡§Î¡¹ Tm" ¡Î¡H(x, y) = 0m'uxOy¡�ÝKÎ¡" ÝÝÝKKKÎÎÎ¡¡¡��AAA��µµµ ±dmO§Ru¤ÝK�I¡. YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK m3I¡þ�ÝK ÝKÎ¡xOy¡��¡m3xOy¡þ�ÝK " 3È©Ú¡È©�O¥§ I(½áN½ ¡3I¡þ�ÝK§ù|^ÝKÎ¡ÚÝK" YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK m3I¡þ�ÝK ÝKÎ¡xOy¡��¡m3xOy¡þ�ÝK " 3È©Ú¡È©�O¥§ I(½áN½ ¡3I¡þ�ÝK§ù|^ÝKÎ¡ÚÝK" YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK m3I¡þ�ÝK ÝKÎ¡xOy¡��¡m3xOy¡þ�ÝK " 3È©Ú¡È©�O¥§ I(½áN½ ¡3I¡þ�ÝK§ù|^ÝKÎ¡ÚÝK" YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK m3I¡þ�ÝK ÝKÎ¡xOy¡��¡m3xOy¡þ�ÝK " 3È©Ú¡È©�O¥§ I(½áN½ ¡3I¡þ�ÝK§ù|^ÝKÎ¡ÚÝK" YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK m3I¡þ�ÝK ÝK�ïÄL§ YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK m3I¡þ�ÝK ~3 ¦�Ô¡y2 + z2 = x²¡x + 2y − z = 0��3 nI¡þ�ÝK§. ) YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK m3I¡þ�ÝK YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK m3I¡þ�ÝK YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK m3I¡þ�ÝK YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK m3I¡þ�ÝK YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK m3I¡þ�ÝK ~4 �áN§dþ¥¡z = √ 4 − x2 − y2ÚI ¡z = √ 3(x2 + y2)¤¤§¦§3¡xOyþ�Ý K" )µ ¥¡ÚI¡�� C :  z = √4 − x2 − y2,z = √3(x2 + y2). �z§�ÝKÎ¡µx2 + y2 = 1" K�C3¡xOyþ�ÝK�{ x2 + y2 = 1, z = 0. ¤¦áN3¡xOyþ�ÝKµx2 + y2 6 1 YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê JJJjjj mmm��§§§ mmm��ëëëêêê§§§ mmm333III¡¡¡þþþ��ÝÝÝKKK � Thank you! YUAN Peng SS, at ZHBIT 111lllÙÙÙ mmm)))ÛÛÛAAAÛÛÛþþþêêê 空间曲线的一般方程空间曲线的参数方程空间曲线在坐标面上的投影

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空间曲线及其方程

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