1、22221212222212222211,1ppppctctpppppct()()jtkxiiAjtkxrrAppeppe()()()()()()() 2cosjt kxjt kjxiArAjt kxt kxjt kxiriArAjt kxjt kxrArij trAArAApppp ep ep ep epp ep eppekxe()()2cosjtj trAkxiArApppkxepe.)2 , 1(2nnxnkx(21)(21)(1,2.)24kxnxnn111222cos()cos()AApptppt12cos()Appppt122221221112211222cos()sinsinar

2、ctancoscosAAAAAAAAAppppppppp220epc12122120cos().AAppc1222212212cos()AAAAAppppp12121220 0,AAAAAp ppppc12121220 0, AAAAAp ppppc1212112112200002, 224AAAAApp pppcc212111212200002, 20AAAAAp ppppcc11112222c o s ()c o s ()AApptppt1212112220 02.cos()cos()AAp pttc12oyxzr22220222222111()(sin)sinsinppppcrtrrrr

3、r2222pcpt)(1222022rprrrctp222022prprctr22222XXctr()()jtkrjtkrXAeBe()( , )jtkrAp r teraZpu ()2001(1)jt krAjkrujkr epjrjr0011rpupdtudtr 200 0022()11 ()1 ()ajrc krrZjjkrkrkraaaaaZrjxrj m2200)(1)(krkrcra200)(1)(krkrcxa20)(1krrmajaaZZ e002cos ,cos1akrZckr1kr221 k r1kr221 k r20 00 02()1 ()ac krrckr002()01

4、()ac krxkr00 01,452aarxc220 00 02()()1 ()ac krrc krkr0 00 02()()1 ()ac krxc krkr200,0,0aarc x00001111ajkrZircjr120 00apppuuuZcjr00001ReRe1 cos()cos()TTmmIpudtTpptkxtkx dtTc220 00 0122mAIpcc r220 00 022mpAIcc r20 02mpIc2220000coscoscoscoseeeeeappIp upZcc2002002221rcAcpIm0022cAWa24aWIdSr I)1(222022rpr

5、rpctp( )j tpR r e22210RRk Rrrr零階貝賽爾方程)()()(0201krNAkrJArRJ0(kr) 零階貝賽爾函數(shù)N0(kr) 零階諾依曼函數(shù)( )J z( )N z1020( )()()j tj tpR r eAJkrA Nkre01,()krJkrkr 0sin14,()krkrN krkr00,()krNkr 1000( )( )( )HzJzjNz2000( )( )( )HzJzjNz0階第1類漢克爾函數(shù)0階第2類漢克爾函數(shù)(2)(1)00( )()()R rA HkrB Hkr(2)(1)0000()()j tpA HkrB Hkre向r增大方向擴張的柱

6、面行波向r=0方向收斂的柱面行波)()()2(0krAHrR(2)000()()()j tj tpA JkrjNkr eAHkr e(2)000(2)(2)01001()()()j tj tj tpjAudtHkr errjAkjAkHkr eHkrekr (2)00 0(2)1101001010 022221111()()aaaHkrpZjcuHkrJ NN JJ JN NcjrjxJNJN 10102Jz NzNz Jzz01010 00 0222211112,aaJ JN NkrrcxcJNJN(2)02()lnj tj tApAHkr ejkr e (2)10 00 021()j tj

7、 tjAAuHkr eecckr 0 0ln()aapZjc krkrjxu(2)(/4)02()j krHkrekr1mpraarcupZ00(2)(/4)02()j tj krj tpAHkr eAeekr(2)(3 /4)10 00 02()j tj krj tjAjAuHkr eeecckr(2)(3 /4)12()j krHkrekr(2)000()()()j tj tpAHkr eA JkrjNkr e(2)11100()j tj tjAkjAkuHkreJkrjNkre 2221001000011( )( )(sincos)TTeeAIRp R u dtJ NtJ Nt dtTT

8、c22221001000 00 02210010 00 02220 00 00 020 011sincos1122122TTmeeAAIJ NtdtJ NtdtTcTcAAJAck rNJ Ncckrppc ucc1Ir()0( , )jt kxp x tA etkxconstpdxcdtk2pkc011022( , )cos()cos()p x tAtk xAtk x212121210( , )2cos()cos()2222kkkkp x tAtxtx1212002121,22,22kkkkkk000( , )2cos() cos()p x tAtk xtk x 0( , )/p xt A0

9、t波 包0載 波載波與波包的波形0載頻，調(diào)頻可得tk xconst gdxdcdtdk,gpdccdkktjaezyxpp),(2222222=0 (2)aaaapppk pxyz(1) 12220222222tpczpypxp)()()(),(zZyYxXzyxpa0)()(3) 0)()(0)()(222222222zZkzzZyYkyyYxXkxxXxxx2222zyxkkkkzkBzkAzZykBykAyYxkBxkAxXzzzzyyyyxxxxsincos)(sincos)(sincos)( ) ( ) ( )j tpX x Y y Z z epju010000001( ) ( )s

10、incos1( ) ( )sincos (4)1( )( )sincosj txxxxxxyj tyyyyyj tzzzzzzjkpuY y Z zAk xBk x ejxjkpuX x Z zAk yBk y ejyjkpuY y X xAk zBk z ejz 0)(0)(0)(),0(),0(),0(zyxlzzlyylxxuuunlkBlnklnklnknlkBnlkBzzzzzyyxxyyyxxx, 0, 0, 0,0 xyzxyznnnnnnpp22200,()()()222xyzyxznnnxyznkccnnflll,coscoscos (5)xyzxyzj tnnnnnnxyzpAk xk yk z ezjkzzeAzZ)(),., coscos (6)zxyxyjt k znnnnxypAk xk y e, coscosxynnxyAk xk y22222,0()() (7)xyzxynnkkkkc 2222,()() xyyxn nxynnll22,20 xynnc(),coscoszxyxyjt