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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
555Lagrangian and Hamiltonian Formulations for Continuous Systems
© 2010 Taylor & Francis Group, LLC
Using this relationship, Equation 16.79 may be rewritten in the relativistically invariant form:
d
d
d
d
d
dx
A
x
A
x
µ
µ
ν
ν
µ
µ
=
0
.
Alternatively, if we dene an antisymmetric second-order tensor F
μν
by
F
A
x
A
x
µν
µ
ν
ν
µ
=−
d
d
d
d
,
the eld equations take the form
d
d
F
x
µν
µ
µ
=
0
.
It can be shown that these equations may be deduced from Hamilton’s principle:
δδLx Lxxxx
dd
ddddd
4
1 234
0
∫∫∫∫
==
with
LF
A
x
A
x
6
2
2
==
∑∑
()
,
µν
νµ
µ
ν
ν
µ
µν
d
d
d
d
.
Other types of vector eld have also been considered. In particular, it has been shown that, as
in the scalar case, complex eld components ...
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Publisher Resources

ISBN: 9781466569980