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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
293Nonlinear Oscillations
© 2010 Taylor & Francis Group, LLC

xx
xx
1
2
10
2
10
+=−−
ωβ
(9.64)

xx xx
xx
2
2
2201
101
2+=−−ωββ
. (9.65)
The initial conditions are
xAx() ()000==
which, in view of Equation 9.44, lead to
xAxi
ii
() () ,,,
...
0000 123== ==
.
From Equation 9.63, the zero-order solution is
x
0
= Acos ωt.
Substituting this for x
0
in Equation 9.64 yields

xxAtAt
At
1
2
1
22
1
2
1
1
2
21
+=−−
=− +−
ωωβω
ωβ
coscos
(cos ) A
At
co
s.
ω
(9.66)
The cosωt term on the right-hand side (which already appears in the complementary solution)
generates the troublesome secular term. We now try to eliminate this term by setting the coef-
ficient of the cos(ωt) term equal to zero; hence,
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Publisher Resources

ISBN: 9781466569980