情形2.两条曲线 相交于点20,它们的参数方程分别为 1(t0)=2(1)1(t0)≠0.=2(0)≠0
/ 2. ü^. C1, C2 u: z0, §ëꧩOǑ: C1 : z = z1(t); C2 : z = z2(t), α 6 t 6 β ¿ z0 = z1(t0) = z2(t ′ 0 ), z′ 1 (t0) 6= 0, z′ 2 (t ′ 0 ) 6= 0. y O x C2 C1 α z 0 (z) v O u α Γ 2 w0 Γ 1 (w) N w = f(z) ò C1, C2 ©ONǑu : w0 = f(z0) ü^ Γ1, Γ2: Γ1 : w = w1(t); Γ2 : w = w2(t), α 6 t 6 β 11/127
情形2.两条曲线 设曲线C1,C2相交于点20,它们的参数方程分别为 C1:z=21(1);C2:z=2(1),a≤t≤β 并且x0=a1(t0)=2(t6),x1(t0)≠0,2(t)≠0 设映射 将C1C2分别映射为相交 f(=0)的两条曲线T1
/ 2. ü^. C1, C2 u: z0, §ëꧩOǑ: C1 : z = z1(t); C2 : z = z2(t), α 6 t 6 β ¿ z0 = z1(t0) = z2(t ′ 0 ), z′ 1 (t0) 6= 0, z′ 2 (t ′ 0 ) 6= 0. y O x C2 C1 α z 0 (z) v O u α Γ 2 w0 Γ 1 (w) N w = f(z) ò C1, C2 ©ONǑu : w0 = f(z0) ü^ Γ1, Γ2: Γ1 : w = w1(t); Γ2 : w = w2(t), α 6 t 6 β 11/127
情形2.两条曲线 设曲线C1,C2相交于点20,它们的参数方程分别为 C1:z=21(1);C2:z=2(1),a≤t≤β 并且x0=a1(t0)=2(t6),x1(t0)≠0,2(t)≠0 设映射=f(2)将C1,C2分别映射为相交于 点0=f(0)的两条曲线r1,T2 I1:=1(t);F2:=2(t),a≤t≤ 口4+23
/ 2. ü^. C1, C2 u: z0, §ëꧩOǑ: C1 : z = z1(t); C2 : z = z2(t), α 6 t 6 β ¿ z0 = z1(t0) = z2(t ′ 0 ), z′ 1 (t0) 6= 0, z′ 2 (t ′ 0 ) 6= 0. y O x C2 C1 α z 0 (z) v O u α Γ 2 w0 Γ 1 (w) N w = f(z) ò C1, C2 ©ONǑu : w0 = f(z0) ü^ Γ1, Γ2: Γ1 : w = w1(t); Γ2 : w = w2(t), α 6 t 6 β 11/127
下面考动C1,C2的夹角与T1,F2的夹角之间的关系 Argul(to)- Arg- g Argo(to)- Arg=(0)
e¡Ä C1, C2 YÆ Γ1, Γ2 YÆm'X: ÏǑ w1 = f[z1(t)], w2 = f[z2(t)], |^/ 1 a qí, k Argw ′ 1 (t0) − Argz ′ 1 (t0) = Argf ′ (z0) Argw ′ 2 (t ′ 0 ) − Argz ′ 2 (t ′ 0 ) = Argf ′ (z0), K Argw ′ 2 (t ′ 0 ) − Argw ′ 1 (t0) = Argz ′ 2 (t ′ 0 ) − Argz ′ 1 (t0). y O x C2 C1 α z 0 (z) v O u α Γ 2 w0 Γ 1 (w) 12/127
下面考虑C1C2的夹角与11,D2的夹角之间的关系 因为1=f{z1(t),2=f[z2(t)],利用与情形1相类 似的推射,有 Argwl(to)-Argi(to)= Argf(zo) Argw2(to)-Argz2(to)= Argf(zo 2(0)-Argm1(t)=Arg=2()-Arg=1(0
e¡Ä C1, C2 YÆ Γ1, Γ2 YÆm'X: ÏǑ w1 = f[z1(t)], w2 = f[z2(t)], |^/ 1 a qí, k Argw ′ 1 (t0) − Argz ′ 1 (t0) = Argf ′ (z0) Argw ′ 2 (t ′ 0 ) − Argz ′ 2 (t ′ 0 ) = Argf ′ (z0), K Argw ′ 2 (t ′ 0 ) − Argw ′ 1 (t0) = Argz ′ 2 (t ′ 0 ) − Argz ′ 1 (t0). y O x C2 C1 α z 0 (z) v O u α Γ 2 w0 Γ 1 (w) 12/127