: P :k n j m i l N + + = .nm l

: l m n

. : ( Cubic Equation) S :03 2213= I S I S I S0 == SSSSzz yz xzzy yy xyzx yx xxij ijo o oo o oo o oo o( )( )( )= + += + += + + 000S n m ln S m ln m S lzz yz xzzy yy xyzx yx xxo o oo o oo o o :

:zz yy xxI o o o + + =1 )) zz yzyz yyzz xzxz xxxyxy xxyyIo oo oo oo oo oo o =2 ( ( ( )2 2 232xy zz zx yy yz xx zx yz xy zz yy xxzz yz xzzy yy xyzx yx xxI o o o o o o o o o o o oo o oo o oo o o+ + + = =( ) 03 2213= I S I S I S : (Real Root) 1 2 3 . l m n

:2 2 21 l m n + + = 1 2 3 (Orthogonal) . . . . : :0 ' ' '3 2213= I I I c c c 12 2 222 2 23'' ( )' . . 2 ( . )xx yy zzxy yz zx xx yy yy zz zz xxxx yy zz xy yz zx xx yz yy zx zz xyIIIc c cc c c cc cc c cc c c cc c c c cc c c= + += + + + += + + + : : 3 2 1 31 3 3 2 2 1 23 2 1 1') ( ''c c cc c c c c cc c c=+ + =+ + =III . :2 2 21 1 1 1 1 1 1 1 12 2 2XX xx yy zz yz zx xyl m n m n n l l m c c c c c c c = + + + + + :1 2 1 2 1 2 1 2 2 1 1 2 2 1 1 2 2 1( ) ( ) ( )XY xx yy zz yz zx xyl l m m n n m n mn n l nl l m l m c c c c c c c = + + + + + + + +

:) (21) (21) (212 1 33 1 23 2 1c c c c c c = = = : ) ( : )) , , () , , () , , (321z r f uz r f uz r f uzruuuu=== : : ( :)1 - z (ezz) :zzzuezc=c2 - r (err) :rrruerc=c : 3 - - (e) : ab AB aI ( ab ) . : 4 - r :1 12rru u uer r ru uuuc c (= + (c c : : 11 121 1212zzzrrrrrrzzz rrzuezueru uer ru u uer r ru uez ru uer zuuuu uuuuuuuc=cc=cc= +cc c (= + (c c c c (= + (c c c c (= + (c c 5 - z :1 12zzu uez ruuuc c (= + (c c 6 - rz :12z rrzu uer zc c (= + (c c : : ((((

zz z zrz rrz r rre e ee e ee e euu uu uu ) ( : )) , , () , , () , , (321 u | u uur f ur f ur f ur=== : : :11cotsin1 1 1( cot )2 sin1 121 12 sinrrrrrrrrrueru ur ruu ur r ruuur ru u ur r ru uur r ruuuuuu u uu cuc uu c uu u cucu c=cc= +cc= + +cc ( c= + (c c c c (= + (c c c ( c= + (c c :((((

u u uu u ue e ee e ee e errr r rr : ) (Compatibility differential equations) eij u v w :xxuexc=c u v w x y z eij

. : eij u v w

. . eij u v w . u v w eij

. eij . . : 0) (21= = =cc+cc=cc= cc=zy zx zzxyyyxxe e exvyueyvexue : u v x y w . u v

. : 2 32 2232 223 32 22 222 21 1( )2 22xxxxyyyyxyxyyy xyxxe u uex y x yev vey x x yeu v u vey x x y x y x ye eey x x yc c c= =c c c ccc c= =c c c cc ( c c c c= + = + (c c c c c c c c c cc + =c c c c : z xey xexez yey xez yeyez xez yex zezey xez yezeyez xezexey xeyexexyxzyzxxyz xyxzyyzxyz xyzzyz yyzzzx xx zzxyxxyyc cc+c cc=cc+c ccc cc+c cc=cc+c ccc cc+c cc=cc+c ccc cc=cc+ccc cc=cc+ccc cc=cc+cc. . .. . .. . ..2.2.2222222 222222222222222222222222 eij u v w : : . exx eyy ezz exy exz eyz u v w . :