DOC.10 RESEARCH NOTES
225
[p. 20]
i
+
¥2
=
x3
(*.
y)
-
-¥i 00
~
dp
11
12
+
13
_
X
=
x
(y,
(y)
+C,)
=
x (+11
+
0
+(Ol
(yz)
Y
=
y
(V, (*)
~
0
=
J
(-
C
+
S)
+ (zx)
z
=
~z (¥1
(?)
-
V2
(z))
=
z
(-
£,
+11)
+
co3
(xy)
Spezialisiert X
=
a
Ist Torsion
Y
-
-ay
& im
Falle z
=
t
gleichformige
Drehung.
Z
=
0
Torsion
ganz
spezieller Fall.
Integrabilitätsbedingungen
x
3 3 Z
XX
3a: 3a:
3xv
Skalar.
32co,
32Öj
, ,
[51]
[eq.
62]
AX
=
0
=
+
cOj
=
a
+
ßy
+
yz
+
8yz
+ e
(y-
z
)
[eq. 63]
5x
=
konst.
+
a1z(&\)
+
ct2y(8z)
ax ay
[52]
+
-
=
2
[eq.
64]
dx
dy
[eq. 65]
dp}]
dp d2X d2X
12
+
=
0
dx2
+
dy2
=
0
[eq. 66] X
=
ayxy
+
a2
(x2
-y2)
+x
[eq. 68]
3xj
dx
ax ax
d2Y
d2Y
P11
=
dx
dy
r
+
r
=
0
[eq.
67]
Y
=
ß^y
+
ß2
(x2
-
y2)
+y
[eq. 69]
dx
dy
P11 =
otjy
+
2
a1y
+
2a2x
+
ß1JC-2ß2y
=
0
[eq.
70]
ßj
=
-2a
«i
= 2ß2
[eq.
71]