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x i=x i(1, 2 , 3)

y i=y i(1 ,2, 3 )

gij= xr

i

xr

j

gij=

i

xr

j

xr

Gij= y

r

i

yr

j

Gij=

i

yr

j

yr

I1=grs

Grs

I2=grs

Grs

I3=grs

Grs

g=|g ij|

G=|Gij|

I3=1

W=W(I1, I2)

ij= gij+Bij+Gij

=2 W/ I1

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=2 W/ I2

Bij=(gij grsg ir gjs)Grs

ij i+ Fj= fj

ij

ni=pj

ij=(Gjj /Gii)1 /2 ij

x1=f(r)cos

x2=f(r) sin

x3=z /

y1=rcos

y2=rsin

y3=z

f

( '(r ))2

0 00 ( f(r ))2

0

g ij= [02 ]

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gij=[(f'(r ))2 0 0

0 ( f(r ))2 00 0 1 /2]

Gij=[

1 0 0

0 r2

0

0 0 1]Gij=[

1 0 0

0 r2

0

0 0 1]

gij=

[1/ 0 00 1/ r2 0

0 0 2]

gij=[ 0 0

0 r2

0

0 0 2]

x1= rcos

x2= rsin

x3=z /

I1=2+2/

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I2=1/2+2

I3=1

Bij=[

+1 /2 0 00 1/2 r2+/r2 00 0 2

] p

r

=r 2

p

=

p

z=0

ij r=

ij,r+rm

i rmj

ijr=grsijs

ijs= 2x

r

i

j

xr

s

p=0.5 r2 2

+ B

11=r 22=

+ (+1 /

2 ) 12

r2

2+B

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33=2+2

1

2r

2

2+B

23=31=12=0

n1=cos

1, n

20,n

1=sin

1

11=!1 , 33 sin 1=!

3"# r=r1 on c$r%& s$rf"c&

!1=0 , r=r1

B=1

2

2r

1

21

(+1 /2 )

11=22=11=r2 22

=

r

(12r2)1

2

2

r

(12r2)+( 21 )+( 12 )

33=1

2

2

33=

1

2

2("2

r2)+(21)+(12 )

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0

2(

0

" /

33

r''r=0

(

21

)+

(

1

2

)+

2

"2

4 =0

!0

3=

2

"2

4

!=2 ( r1!

3= 1

2(( " 22 sin

1) r

1)

W=*1(I13 )+*2(I23)

4++ 3+(n21 )+=0

r

(12r2)

11=22=1

2

2

33=

1

4

2[(2 r12"2

1)2r2]

33=

1

4

2 [( 2 r12"2 )2 r2 ]

12=

23=

31=0