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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
550 Classical Mechanics
© 2010 Taylor & Francis Group, LLC
Again, conditions (δq)
1
= (δq)
2
= 0 have been used. In Equation 16.56, we have written a total
time derivative with respect to x
i
in order to emphasize the fact that the derivative involves not only
the explicit dependence of £ on x
i
but also the implicit dependence on x
i
through q. Substituting
Equations 16.55 and 16.56 into Equation 16.54, we obtain
δq
L
qt
L
qx
L
qx
dd
i
d
i
i
∂∂
=
d
d
d
d/
()
1
3
dddddxxxt
123
0
=
∫∫∫
. (16.57)
Now, the variations q(x
1
, x
2
, x
3
, t) are completely arbitrary, so Equation 16.57 is satised if and
only if the integrand vanishes identically:
d
d
d
d/t
L
qx
L
qx
L
q
d
i
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Publisher Resources

ISBN: 9781466569980