1£®ÔÚ¸ºÔØz = 0´¦£¬·´É䲨µçѹÓëÈëÉ䲨µçѹµÈ·ùͬÏ࣬ºÏ³É²¨µçѹΪVLcos£¨¦Øt£©,ÆäÕñ·ùVL ÊÇÈëÉ䲨¼´·´É䲨µçѹÕñ·ùµÄÁ½±¶£»¶øÔڸô¦·´É䲨µçÁ÷ÓëÈëÉ䲨µçÁ÷µÈ·ù·´Ï࣬ºÏ³É²¨µçÁ÷Õñ·ùΪÁã¡£
2£®ÓÉÓڵȷùµÄÈëÉ䲨Óë·´Éä
²¨Ï໥µþ¼Ó£¬ÑØ´«ÊäÏß·½Ïò ºÏ³É²¨µçѹµÄÕñ·ù°´ÓàÏÒº¯ÊýµÄ¹æÂÉ·Ö²¼£»¶øºÏ³É²¨µçÁ÷µÄÕñ·ù°´ÕýÏÒº¯ÊýµÄ¹æÂÉ·Ö²¼¡£Õâ˵Ã÷£¬ÓëÄ©¶Ë¶Ì·µÄÀíÏë´«ÊäÏßÒ»Ñù£¬Ä©¶Ë¿ªÂ·µÄÀíÏë´«ÊäÏßÉϵçѹ¡¢µçÁ÷µÄÕñ·ù·Ö²¼Ò²¶¼³Ê´¿×¤²¨·Ö²¼¡£ 3£®ÔÚËùÓÐz?n?p2
ͼ1.4-2 Ä©¶Ë¿ªÂ·µÄ´«ÊäÏßÉϵçѹ¡¢µçÁ÷ºÍµÈЧ×迹µÄ·Ö²¼
´¦ºÏ³É²¨µçѹÕñ·ù×î´ó£¬ºÏ³É²¨µçÁ÷Õñ·ùΪ
Áã¡£ÕâЩλÖÃÊÇ´¿×¤²¨µçѹµÄ²¨¸¹µã£¬´¿×¤²¨µçÁ÷µÄ²¨½Úµã¡£ ?p4£®ÔÚËùÓÐz?(2n?1)´¦£¬ºÏ³É²¨µçÁ÷Õñ·ù×î´ó£¬ºÏ³É²¨µçѹÕñ
4·ùΪÁã¡£ÕâЩλÖÃÊÇ´¿×¤²¨µçѹµÄ²¨½Úµã£¬´¿×¤²¨µçÁ÷µÄ²¨¸¹
37
µã¡£
5£®Ä©¶Ë¿ªÂ·µÄÀíÏë´«ÊäÏßÉϵÄÈÎÒâ¹Û²ìµã´¦£¬µçѹºÍµçÁ÷Ö®¼äÒ²ÓÐ90¡ãÏàλ²î¡£ÓëÄ©¶Ë¶Ì·µÄÀíÏë´«ÊäÏßÏàËÆ£¬Ä©¶Ë¿ªÂ·µÄÀíÏë´«ÊäÏßÉϵçѹ¡¢µçÁ÷½»Ìæ´ïµ½Õñ·ùÖµºÍÁãÖµµÄʱ¼ä¼ä¸ôÒ²¶¼ÊÇ1/4ÖÜÆÚ¡£
6£®Ä©¶Ë¿ªÂ·ÀíÏë´«ÊäÏßÉϵĸºÔØ·´ÉäϵÊýºÍÈÎÒâ¹Û²ìµãµÄ·´ÉäϵÊý·Ö±ðΪ
?£Ì£½1 ºÍ ? ( z)??Le?j2?z?e?j2?z (1.4-15) 7£®Ä©¶Ë¿ªÂ·µÄ´«ÊäÏßÉÏÈÎÒâ¹Û²ìµã´¦µÄµÈЧ×迹Ϊ
Z(z)?ZL?jZ0tan(?z)Z0?jZLtan(?z)ZL????jZ0cot(?z)?jX(z)
£¨1.4-16£© ¶ÔÓÚÄ©¶Ë¿ªÂ·µÄÀíÏë´«ÊäÏߣ¬ÓÉÓÚÈÎÒâ¸ø¶¨¹Û²ìµã´¦µçѹºÍµçÁ÷Ö®¼äÓÐ90¡ãÏàλ²î£¬Òò´ËµÈЧ×迹ҲΪ´¿µç¿¹£¬ÇÒ°´ÓàÇк¯Êý¹æÂÉ·Ö²¼¡£
±È½ÏÄ©¶Ë¶Ì·ºÍ¿ªÂ·µÄÀíÏë´«ÊäÏßÉϵçѹ¡¢µçÁ÷·Ö²¼±í´ïʽ£¬×迹·Ö²¼±í´ïʽ£¬ÔٱȽÏͼ1.4-1ºÍͼ1.4-2¿ÉÖª£¬ÑØ´«ÊäÏß·½Ïò¿´£¬Á½ÖÖ״̬ϵĵçѹ¡¢µçÁ÷ºÍ×迹µÄ·Ö²¼¾ù´í¿ªÁË1/4¸öÏನ³¤¡£Òò´Ë£¬ÔÚʵ¼ùÖг£³£ÓöÌ·´«ÊäÏßÀ´´úÌæ¿ªÂ·´«ÊäÏß¡£ÓÃÀ´´úÌæ¿ªÂ·´«ÊäÏߵĶÌ·´«ÊäÏßÉϾàÀë¸ºÔØ1/4¸öÏನ³¤
38
´¦ÊÇ´¿×¤²¨µçѹµÄ²¨¸¹µã£¬´¿×¤²¨µçÁ÷µÄ²¨½Úµã£¬µÈЧ×迹ΪÎÞÇî´ó£¬¸ÃµãÓÖ³ÆÎªµÈЧ¿ªÂ·µã¡£°Ñ¶Ì·´«ÊäÏßÉϵĵÈЧ¿ªÂ·µã¿´³ÉÊÇ¿ªÂ·´«ÊäÏßµÄÄ©¶Ë£¬¾Í¿ÉÒÔÓÃÕâÌõ¶Ì·´«ÊäÏßÀ´´úÌæ¿ªÂ·´«ÊäÏß¡£
3£®Ä©¶Ë½Ó´¿µç¿¹¸ºÔصÄÀíÏë´«ÊäÏß
ÀíÏë´«ÊäÏßÄ©¶Ë½Ó´¿µç¿¹¸ºÔØZL?jXLʱ¸ºÔØ´¦·´ÉäϵÊý¼°ÆäÄ£·Ö±ðΪ
?L?ZL?Z0ZL?Z0ZL?iXL?jXL?Z0
jXL?Z0?L?2Z02?XLZ0?XL22?1
·´ÉäϵÊýµÄģΪ1Òâζ×Å´«ÊäÏßÉÏ·¢ÉúÈ«·´É䣬¼´Èë¡¢·´É䲨µÄÕñ·ùÏàµÈ£¬ËùÒÔ£¬ÔÚÈë¡¢·´É䲨·´ÏàµÄλÖô¦¶þÕßÏàÏûΪÁ㣬ºÏ³É²¨ÈÔΪ´¿×¤²¨¡£ÓëÖն˶Ì·ºÍ¿ªÂ·²»Í¬µÄÊÇ£¬ÔÚ¸ºÔØ´¦¼È²»Êǵçѹ²¨½Úµã£¬Ò²²»Êǵçѹ²¨¸¹µã£¨Öն˶Ì·ʱ¸ºÔØ´¦Îªµçѹ²¨½Úµã£¬ÖÕ¶Ë¿ªÂ·Ê±¸ºÔØ´¦Îªµçѹ²¨¸¹µã£©¡£´Ëʱ£¬´«ÊäÏßÉϺϳɵçѹµçÁ÷·Ö²¼¹æÂÉÓëÖն˶Ì·ºÍ¿ªÂ·Ê±ÀàËÆ£¬Ö»ÊÇÔÚλÖÃÉÏ´í¿ªÁËÒ»¶¨µÄ¾àÀ룬ÈçͼËùʾ¡£
¶ÔÓÚ´¿µç¸ÐÐÔ¸ºÔصÄÇé¿ö£¬Öն˵ĵç¸Ð¿ÉÓÃÒ»¶Î³¤Îªz0µÄÖն˶Ì·ÏßÀ´´úÌæ¡£¸ù¾ÝµÈЧ¹ØÏµ£¬µÈЧ³¤¶Èz0Óë¸Ð¿¹XLµÄ¹ØÏµ
39
Ϊ
¼´
jXL?jZ0tan(?z0)?p?pXLXL z0?arctan()?arctan()??Z02?Z041ÁíÍ⣬Öն˵ĵç¸Ð»¹¿ÉÓÃÒ»¶Î³¤Îªz0'µÄÖÕ¶Ë¿ªÂ·ÏßÀ´´úÌæ¡£¸ù¾ÝµÈЧ¹ØÏµ£¬µÈЧ³¤¶Èz0Óë¸Ð¿¹XLµÄ¹ØÏµÎª
¼´
jXL??jZ0tan(?z0)'?p?p?p?p?XLXL ?z0'?arctan()??arctan()?2?Z022?Z041¶ÔÓÚ´¿µç¸ÐÐÔ¸ºÔصÄÇé¿ö£¬Öն˸ºÔØ´¦ºÍÈÎÒâλÖô¦µÄ·´ÉäϵÊý·Ö±ðΪ
jXL?Z0ej(???)?L??j??ej(??2?)
jXL?Z0eLLL?(z)??Le?j2?z?ej(??2?L?2?z)
ʽÖУ¬?L?arctan(Z0)¡£ XLͬÀí£¬¶ÔÓÚ´¿µçÈÝÐÔ¸ºÔصÄÇé¿ö£¬Öն˵ĵçÈÝ¿ÉÓÃÒ»¶Î³¤Îª
z0µÄÖն˶Ì·ÏßÀ´´úÌæ¡£¸ù¾ÝµÈЧ¹ØÏµ£¬µÈЧ³¤¶Èz0ÓëÈÝ¿¹XCµÄ
¹ØÏµÎª
40