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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
288 Classical Mechanics
© 2010 Taylor & Francis Group, LLC
xt
bn
t
n
n
() cos(
)
=
=
ω
0
. (9.38)
The symmetry of the potential function means that both even and odd n are present in Equation
9.38. The determination of b
n
can be made in the same way that we did for the symmetric case, with
the result
b
mn k
xk kx nt t
n
=
+
1
22
1
2
23
0
2
πω
ωω
π
()
()cos( )(
)
d
.
(9.39)
If third-order accuracy is maintained, Equation 9.39 leads to
b
k
k
bb
mk
kbbkbb kb
0
1
3
1
2
1
2
1
201212 31
3
1
2
3
4
=− =
++
,
ω

(9.40a)
b
mk
kb b
mk
kb
bk
b
2
2
1
21
2
3
2
1
21
23
1
3
1
24
1
9
1
4
=
=
+
()
,
ωω

(9.40b)
and the approximate Fourier series solution is
xt
k
k
bb t
k
k
bt
k
k
k
() co
sc
os=− ++
++
2
1
1
2
1
2
1
1
2
2
2
1
3
6
2
48
ωω
332
3
1
1
3
k
bt
co
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Publisher Resources

ISBN: 9781466569980