DOC.
47
295
where
l', m',
n'
denote the direction cosines
of the
normal (directed toward
the interior of the
body), and sx', sy', and
sz'
the projections
of s'.
From
equations (2)
it follows that
s'x
=
sx
s'y
=
ß.Sy
S'z
=
ß.sz,
where
sx,
sy,
sz
are
projections of the surface
element
with respect
to S.
For the
components
Kx
,
Ky
,
Kz
of the
pressure
forces with
respect to
S,
we
therefore obtain
from
the last three
systems
of
equations
JT
=
Kl
=
p]sl
=
=
p]-s
cos
t
X X
r
X
*
X
r
Ky
=
|
Ky
=
ip's'y
=
p'-sy
=
P'-s'cos
"
Kz
=
I
Kz
=
I
p'sz
=
p''sz
=
p''s'cos
n
where
s
is the
magnitude
of the surface element,
and
l,
m, n
denote the
direction cosines
of
its
normal
with respect
to
S.
We
thus obtain the result
that the
pressure
p' with respect
to
the
co-moving system
can
be
replaced
with
respect
to
another reference
system
by a
pressure
that
has
the
same
magnitude
and
is also
perpendicular to
the surface
element.
In
our
notation
we
thus
have
p
=
p0
.
(22)
Equations (16c), (29),
and
(22)
enable
us
to
determine the
state
of
a
physical
system
using
the
quantities
E,
V,
p,
which
are
defined with
respect
to
the
same
system
as
the
system's
momentum
G
and
velocity
q,
instead of
using
quantities
E0,
V0,
p0
referred
to
the
co-moving
reference
system.
E.g.,
if
to
a co-moving
observer the
state
of the
system
under