绪论及基础知识

1、1 2 2 2 v pconst LV c A ndA 0 D Dt 3 4 n V 1 1V a 21 VV 12 0 sh Dm VV 5 6 7 8 PRT 9 10 11 12 13 14 DVp R Dt 2 2 V pconst 11211 2 3 11121 2 3 y xxxxz x yyyy xz y v Dvvvvvp RV Dtxxxyyxzzx Dvvvv vvp RV Dtxyxyyyzz 11112 2 3 y xzzzz z y v vDvvvvp RV Dtxzxyyzzzz 15 0,0 uu au xf x tx 1 12 1 nn nn jjnn jj j

2、j n nn jj j uu uu uutOtOt ttt uu u Ox xx 11 11 0 ,0 nnnnnnnn jjjjjjjj jj t uuauuuuuu aOtxx tx uf 16 17 2 2 Vp gzconst DVp R Dt 0V t 2 2 2sin 0.5 p pp C V 222 2 222 0 uuu u xyz 18 2 0V 2 0 DVp R Dt 19 LV 20 21 22 a 或 aL a 3 93 0 10 10 acm cm 23 0 , , ,lim mdm x y z t d md 24 0 lim p pdp K d 2 11 11 1

3、 d d dpa Kdp d dp 2dV d Ma V y T(y+ y) x y T(y) Qy y y y Q dT q Sdy qT 25 y F h v(y) AB x v FdV Sdy f f dtgddv dtdtdy d dt dv vdy dt dy vdt ddy T 26 b Rm 或 00 , , ,limlim bbb xyz m RRdR R x y z tR iR jR k md RdRd bb dRR , , ,R x y z tgk Z X Y kd b dRg n p nn p n p 0 , , ,lim n n S p px y z t S n n p

4、 nn p dsp ds dV dy n p nn p n p 0dV dy 0 n p nn pp n 27 pRT , ,T p , ,u h s , ,0pp Tuu Tf T p , q w uu T hupu TRTh T 1 1 qdupd qdhdp 2 1 2 1 21 21 T T const T ppppp T p const qdu CduC dTuC dTC TuCTT dTdT qdh CdhC dThC dTC ThCTT TdT 28 1 1 p pvpv v pv kR pp C hudhdudC dTC dTRdTCCR k R C kCC k 5 3 2 1

5、.4 72 2 v p CR uRTRTk CR 2 2 2 2 exp3 2 exp1 3 1 2exp111 exp3 1 2 exp1 ve ve v vevv ve pp v ve ve ve ve TTT cRRR T TTccT RT uRTRTccT c TTk kk TR TTT T TT NONO NNe OOe NONOe 29 rev q ds T 21 12 22 11 111 lnln 1 1 1 lnln vv p p q dsd TdT dsdupdCRsCRT TTT qdupd q Cds Tpdpdp dsdhdTRsCRT TTpTp qdhdp 11 1

6、1 21222222 12111111 11 22222222 11111111 1 0lnlnlnlnlnln 1 0lnlnlnlnlnln 1 kk v v kk kk p p k CTTTTT CR TRTkTTT C TppTTTpTkp CRconst TppRTkTTpT 0ds 11 1 lnlnlnln kk kk kk vpv scTCcTpCcpCRTpC 30 R R cossin sincos LNA DNA 2 1 2 qv / 2 w LDMpf LDM ppLDM CCCCC q Sq Sq Slqq LDM ccc q cq cq c 31 Z X Y A O

7、 B dA AdA C , ,A x y zxiyjzk AAA dAdxdydz xyz dAdxidyjdzk Axi xiyjzkixi xxxx j i k r X Y O r=constr+dr=const =const +d =const d e e e r e r e r e d , , rz A rzreze rz dAdrerd edze r rzrr r rzr rz AAA dAdrddz rz eAr rezeere rrrr eAr rezeerre dAdrerd edze dA r r e e e e Z 32 R e n R RdR dR dn 1 dR PP1

8、 Q =const + d =const ijkijk xyzxyz ijk xyz ddxdydzidxjdykdzijk xyzxyz ddR 11 0ddRdRconst 等势面 cos ,cos R R ddRe dR nd dnendRdn n n + d =const间最小距离间最小距离 RR d ddRe dRe dR 1 rz rz ddRdrerd edze eee rrzddrddz rz 33 VVV VijkVijk xyzxyz y xz y xz y xz ijk v vv i xxx Vv vv j yyy v vv k zzz xyz y xz y xz y x

9、z ivjvkv v vvV ijk xxxxx v vvV ijk yyyy v vvV ijk zzzz VDSA 11 ()() 22 11 ()() 22 11 ()() 22 1 0( 2 y xxxz y xz yyyy xxzz yy xxzzzz y v vvvvV VV xxyxz xxx Vvvv VvVv yyyyxyyz Vv VvVvvv zzzzxzyz v x 1 )() 2 11 ()0() 22 11 ()()0 22 xxz yy xz y xzz vvv yxz vv vv yxyz v vvv zxzy 34 0 lim s A nds A dsn V

10、V ds n 0 00 1111 lim 1 limlim s t s s V t nds dd dV nds dtdtt V nds d V dt V ds n yy zxzx vv vvvv yzzxxy xyz ijk Vijk xyz vvv AAL ndAV ndAV dr 35 s s s n dsd n adsad nadsad a 222 2 222 xyz n 2 22 22 11 11 rzrz rrr rrrrz eeeeee rrzrrz eee eeeeee rrrrrrrzrrr 22 22 22 2 22 11 11 , 111 z rrrr ee rrzz rr

11、rrrz 2V VVV 36 37 212121 1 1 2121 11 , , , , ,x y z tx y z txxyy xy zztt zt 高阶项 21212121 21212121 21212121 limlimlimlim tttttttt xxyyzz ttxttyttzttt 21 21 21 21 lim 12 tt D Dttt tt 点与 点趋向重合 212121 212121 212121 limlimlim xyz tttttt xxyyzz VVV tttttt xyz D VVVV Dtxyztt D V Dtt t V V Vt V V t 38 , , ,

12、Ix y z t d 2 2 Id IVd V Ied IrV d (t) (t+ t) S S2 n V t 3 S1 n dA dA V t 2 1 31 00 limlim t tt tt IttItIttItt DI tI ttI tD d DtDttttt 12123313 ttt 0 lim tt t IttIt dd ttt 311 12 000 limlimlim S SSttt tV ndA IttItt V ndAV ndA ttt dtV ndA A D ddV ndA Dtt 39 A D V Dtt D ddV ndA Dtt s A a ndsad V ndAV d

13、 D dVd Dtt F 0 0 DFDDFD F dFV dFFV d DtDtDtDt DDF F dd DtDt VVV 0 0 DD dVV dV d DttDt DD 0VV=0 DtDt D dd Dt 40 41 0,0 uu au xf x tx 1 12 1 nn nn jjnn jj jj n nn jj j uu uu uutOtOt ttt uu u Ox xx 11 11 0 ,0 nnnnnnnn jjjjjjjj jj t uuauuuuuu aOtxx tx uf 42 LV 43 44 1 1 p pvpv v pv kR pp C hudhdudC dTC dTRdTCCR k R C kCC k 5 3 2 1.4 72 2 v p CR uRTRTk CR 2 2 2 2 exp3 2 exp1 3 1 2exp111 exp3 1 2 exp1 ve ve v vevv ve pp v ve ve ve ve TTT cRRR T T