DOC.
8 ANALYSIS
OF A RESONATOR'S MOTION
225
»"'7*
A/2,,v
-
A\t
|l
-
2-cosp1
or,
since
we
have to
relate
everything
to
the
proper frequency
v0'
of the
moving
oscillator
/ 2
v/7*
"
./
,
^l1
"2|COSPl)
=
A
i
v0Ml +
-cosfj
XT
V
+
vo'
7
008
*
c
*f)
-fi-2rcoSJ.)cv
-
/v0r
Furthermore,
we express
the
quantity
A2T
in terms
of the
mean
radiation
density
p.
We
set
the
mean energy
of
a
plane
wave coming
from
a given
direction
equal
to
the
energy
density
in
a
cone
with
a
solid
angle
dK. If,
in
addition,
we
also
keep
in mind
that the
magnetic
and
the
electric
forces
are equal,
and take
into
account
the
two
planes
of
polarization,
we
arrive at
the relation
dK
1
A2T
~
7
p
-
=
*2 *2.
4* 8*
2
Our
expression
for the
force
becomes
(8)
F
=
3c2
16h2
2v0'
Pv'
+
V0
/
(a?L
v
cos
(p^
-
-
1
-
sin2pj
sin2
to
v
1
-
2-cos
^
c
dK.
Finally,
integrating
also
over
all solid
angles,
we
obtain the total
force
that
we were
seeking:
(9)
K
=
-
3
co
lOitv^
v
§3.
Calculation of
the
Fluctuations of Momentum
A2
The
calculation
of the
momentum
fluctuations
can
be made
considerably more simple
than the
calculation
of
the
force
because
a
transformation
according
to
the
theory
of