106
DOC.
1
MECHANICS
LECTURE NOTES
do,
dt
-
co
sin
cp
ov =
L
d^
dt
+
co
sin
cpox
+
co
cos
cpoz =
M
do.
Tt
-
co
cos
cpov =
N[67]
[p. 106]
N
=
0 because reaction of the
guide
normal
oz
oo
klein
ox
=
Oq
cos a
L
=
-M
sin
a
M
=
+
M
cos a
ov,
=
o0
sin
a
N
=
0
do.
dt
-
co
cos
cpo0
sin a
,
da.
d2
a
Iz
-^2
=
03
cos
sin
a
We
also
introduce
ß
=
u
-
o
d2$
ojcos
p
o0
.
--
=
-sinß
dt2
I
°0 =
Jr«'
This
is
the
pendulum equation.
If the
initial
rotation about the
Z-axis
is
small,
then
oscillation
of the
pendulum
about the
northerly
direction
with oscillation
period
T
=
27t
I
1
Ir
COS(p
!»'
Example
Iz
=
Ir
p
=
0
a'
=
2n
•
100
T
=
29.4.
For the
calculation
of the
moment
of reaction
we use
the
first
or
the second
equation
of
motion.