DOC.
10
RESEARCH NOTES
203
[eq. 3]
3
2
yAy
-
^
grad
y
=
0
UmfoTransformieren
[5] [p. 2]
r
3G44
[eq.
4]
OXa
=
0
a
14
3A:'j
24 3x
2
G'
a Aag4
A
p
g p4
"+
*
+
^paßp^ßon
k+G44
X
4X.ß4|x
^44 =
P
o
r Tensor der
G [6]
Wahrscheinlic
Div T
=
0.
Ist dies invariant?
I
3G
X[l
I
n
a
=
o
X
=
1234
a
^
3A'
X
X
p
G
-
a,}
=
0
pG pA G[1J
Alles
nur
von
x1
und
x2
(Zeit) abhängig
[7]
Gn
=
G'a2
+
G'
(2a1ta0l) +
G'
0a2
Ii ii~ii
12 v 11 21
22
21
G,,
= n
/
X
1
*2/
*lail
«21
*2 a21
a22
[eq.
5]
[eq. 6]
G,
2
=
G'1,a11a1, +
G'1,(a,1a,,,
+
a,la1,)
+
G',,a,,a22
pa
pa
pl
al
111112
12
v
11
22 21
12
22
21
G"
=
G22
=
G'naJ0 +
G')0 (a10a00
+
a00a10)
+
G%0a2222
12
=
1«pa
=
G'lia?
+
G'l2(aHa21
+
anal2)+G22o?2X
11 12 12
v
12
22 22
12
G22
~
a
11
20tlia21
a
21
x2
=
(anX|
+
a12x2) 2(+a13A'3
+
a14^4
)2)
=
aznx\
+ 2xxx2anaxl +
x2
2 2
2^2a
12
r'
r'
12
(anAj +
a12x2)
(a21Xj-f
a22x2) =
x2x
(anot21
+
xxx2{ana22
+
a12a21) +
x2a12a22
a
(ail
+a2l)2*l
21
X
x
=
OCjj-XJ
+
OC12^2
dxx
=
a
+ a
udx\
21dx'2
/
d2
V
dx
?
a
=
axx--
+
2a,,
a
l
32
/
dx'2
11
2ldx\dx'2
X
2 ~
a21Xl
+
a22X2
dx
=
a
+' a.
l2dx\
~22dx'2
ax4
-
G41
r
=k+
in,