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1、 J.Sys.Sci.&Math.Scis.26(4)(2006,8),395–401 ∗( 100081)( 100080)
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2、5,53-041 [1])1979 !!""#$ *% &'+($%.),) ! &$%'-*+. , -, .(/Æ0/Æ#)*"#0+*%0,$-1993 [2].)1&'1(Ritt-Wu223#1*/+ 3)*44!5+5-1995 [3],Seidenberg-.#,/, .60!76$% 71$%)9: "#$ *%$-0;-1 [4]+.9: -"#$ *%8< 2=>3 -?2$3*44 ,$1*6"#-1998 [5].Clifford4+9@$% -*+.9: A5"#
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4、502C05)FGLGNHOPI2005-05-12.396QRHISH262J !KLMN"JO#P$QR%S& -# TTB UOTGA< -B(V BP;LB ;),VT 0CB(V ;LP;);Q1$- -#RW*W (V ;)B7XSMY -XZB-ED)8< -# YT [AUN -0 -B-Z(u,v)D9: -R(u,v)VO+ [ {R;e1,e2,e3}D -P\VQWR ]e1,e2!SD]Ru,RvP
5、e2,(1)⎨de1=ω1e2+ω13e3,(2)⎪⎪de2=−ω1e3+ω23e3,(3)⎩de3=−ω1e4−ω23e2.(4)Gauss$3D⎧⎨dω1=ω12∧ω2,(5)dω2=ω1∧ω12,(6)⎩dω12=−Kω1∧ω2.(7)VWdω1dω2ω12=ω1+ω2.(8)ω1∧ω2ω1∧ω222ZE,GD -U1X?2B YRu=E,Rv=G,^√√ω1=Edu,ω2=Gdv.(9)^_e1,e2D -@$< T{R;e1,e2,e3}D -UXXQWR-^ω13=k1ω1,ω23=k2ω2.(10)Zr(s)D -# sD ZYO+ {r;
6、T,N,B} FrenetQWR U=+$3D⎧⎪⎪r˙=T,(11)⎨T˙=kN,(12)⎪⎪N˙=−kT+τB,(13)⎩B˙=−τN,(14)r˙]8:r(s)AZYO+s;Z-9: r(s)FrenetQWR[TN[ r(s)]) -R(u,v)#`F-MY:1>a5] r(s)&'Q1*QW-{r;T,e,e3},]e=e3×T,TD ) -#BQWR-U=+$3D⎧⎨T˙=kge+kne3,(15)e˙=−kgT+τge3,(16)⎩e˙3=−knT−τge.(17)D]^1QWR,:GÆ>a8:.* ED_+1*O+θ∈[0,
7、π].U5T[e1^_ YT=cosθe1+sinθe2.(18)4b`_`aaI397`BQW"a [e=−sinθe1+cosθe2.(19)ckn,kg^1YD6Ykgsinθe1−kgcosθe2−kne3N=−.(20)kg2+kn2knsinθe1−kncosθe2+kge3B=.(21)k2+k2gndb(1)0(18)7 [ω1=cosθds,ω2=sinθds.(22)db(9)0(22),[cosθsinθdu=√ds,dv=√ds.(23)EG`(15)0(16),[⎧⎨kgds=dT·e,(
