DOC.
10
RESEARCH NOTES
257
Für infinitesimale Transformation
3*
pa
dn
dx,
+
pa
dn
8nry
a
a
dxT
ÖGa
8
dx.
öPa
[eq.
187]
Durch Addition
aus
allen drei Termen erhält
man
$
+
pax
fdn
g
pa
xa
dn
\
dx
+
a a
a
dx,
+
•
+
oder
_
+
2
pax
3ji
aa xa
3jt
[121]
8Pa
dx,
+8
a a
3jc
?xa
pa
5*
[eq. 188]
Die Klammer soll für alle Kombinationen
von
pax
verschwinden.
[120][Eq.
186]
results from
transforming
giK, l
under
a
coordinate transformation
to
yield
[eq.
184]
and
then
inverting in
[eq.
185] by
the
tensor
transformation
law.
[Eq. 186]
reduces
to
[eq.
187]
if the transformation
pil
differs
infinitesimally
from the
identity.
[121]Permutation of indices
and
summation
in
[eq.
187]
gives
[eq.
188]
for the infinitesi-
mally
transformed and then
tensorially
inverted
£pox
of
[p.
45].
[Eq.
188]
should
equal
dpox
if d transforms
tensorially
under the
transformation, and
thus the
term
in
the
square
brackets should vanish.
d
1
3?u.v
uxn
2
V
^vß®aß
n n
I
d
^(Yna0aJ+2ä7:0aß
dx^
dxv
0aß
= P0^na^vß-^-^-
^|iv Po
dx^
dxv
dx dx
^nv
dxm
^W^vß
~
«ß
dy'|ia
^nv^T"
YvR®aß'vß
vv
[p.
47]
Kraft auf ruhenden materiellen Punkt
n
=
1
3yaß
0 0 0
0 0
ß
0
ß
2ax
0
aß
Po
dx
dx
0 0 0 0
0 0 0
1
's/o 44