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Classical Mechanics, Second Edition, 2nd Edition
book

Classical Mechanics, Second Edition, 2nd Edition

by Tai L. Chow
May 2013
Intermediate to advanced content levelIntermediate to advanced
639 pages
23h 12m
English
CRC Press
Content preview from Classical Mechanics, Second Edition, 2nd Edition
362 Classical Mechanics
The physical force acting on the bob is the vector sum of the tension
T
in the cord and the weight
of the bob
mg
eff
. If we neglect the centrifugal force term, then

gg
eff
, and the equation of motion
of the pendulum bob is
m
r
t
mg Tm v
δ
δ
ω
2
2
2
=+
−×
. (11.65)
It is clear from Figure 11.19 that the components of
T
are
T
b
/T = b/l or T
b
= bT/l
T
x
= −xT
b
/b = −xT/l, T
y
= −yT
b
/b = −yT/l, T
z
= (lz)T/l. (11.66)
Equation 11.65 then reduces to
mx
x
l
Tmzy
my
y
l
Tm


=−
=−
2
2
ωλ λ
ω
(cos sin)


=
−+
x
mz
lz
l
Tmgmx
sin
cos
λ
ωλ
2
. (11.67)
A fourth equation that relates x, y, and z is provided by the constraint equat ...
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Publisher Resources

ISBN: 9781466569980