DOC.
1
MECHANICS LECTURE NOTES
105
Here
we
assume;
that the
mass
acts
as
if
it
were
concentrated
on
the
bulge, p
is
mean
density.
The
mean
annual
torque approximately
one-half of the
one
calculated
in this
way.
One
thus arrives at
a
value
of
p'
that
is
of the
same
order of
magnitude
as
the
one
observed.
-
Imr/jW
""P
hence
-
M
=
-K"M Cp
3 g
fl3
2it M
T
la'
sinß
T
can
be
calculated.
Mi2
2
5
[66]
Foucault's
Gyroscope
[p. 105]
We
investigate
general
motion of
a
rigid body
at
a
fixed
point
with
respect
to
a
coordinate
system
which
itself
rotates
but
is
not
rigidly
connected
with
the
body
under
consideration.
The
analysis
is
wholly analogous
to
that
applied
in
establishing
Euler's
equations.
The
system
Xx
Yx
Zx is introduced, which
momentarily
coincides with
the
system X Y
Z but
does not rotate
together
with it.
Then the
law
of
moments will
apply
*
\
-
(a)
-
LT
dt
K
If
we
denote
by
p q r
the instantaneous rotation of
X
Y
Z,
then
we
have
dt
daj
dt
+ qaz
-
roy,
so
that the
law
of
moments
reads
dax
dt
da,
dt
do,
dt
+ qoz-
roy =
L
+
rax
-
paz
=
M
+
P«v
-Wx
=
N
Specifically
for
a
point
on
the
surface
of the
earth[67]