224
DOC.
8
ANALYSIS
OF
A
RESONATOR'S MOTION
[14]
(7)
3c2
x
16n2
nA~
3c2
0
A2
T sin
pcosw.
16z2
v0T
2v0
This
is
the
mean
value
of
the
x-component
of the
force
that
a wave
incident
in
the
p,w
direction
exerts
on
the
oscillator at rest.
If the oscillator
is
moving
in
the x-direction with
the
velocity
v,
then
it
is
more
practical
to
replace
the
angles
p,w
with
the
angle
p1
between the
ray
and
the
x-axis,
and the
angle
w1
between the
projection
of the
ray
on
the
yz-plane
and
the
y-axis.
The
following
relations then
hold:
cosc1
=
sin
(p
cos
o),
sin
(pj
cos
Gjj
=
sinpsinw,
SHKpjSinCDj
=
cosp.
We
are
led
to
the
value
of the
force
kx
acting
on
the
moving
oscillator
by
the
transformation
formulas
of the
theory
of
relativity8
V
A' =A(1
- _cospj,)C
T'
=
T(1
+
=
-
v
coscpj
-
_
c
COS
(ft =
*!
=
(xv
- -COSCPj
c
We then
get
-
3c2
o(i
2v0'
-
sin2p1' sin2w11)cosç1'
Neglecting
the
terms
with
(v/c)2,
we
get
[16]
8
A.
Einstein,
Ann.
d.
Phys.
17
(1905):
914.