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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
572 Appendix 1
Each integral on the right-hand side requires for its execution more than knowledge of the limits.
In fact, the three integrals on the right-hand side are not completely dened because in the rst
integral, for example, we do not the know value of x
2
and x
3
in A
1
:
IAxx
xx
P
P
1112
31
1
2
=
(, ,)d .
What is needed is a statement, such as x
2
= f(x
1
), x
3
= g(x
1
), that species x
2
, x
3
for each value
of x
1
(so specify the path of integration). The integrand now reduces to A
1
(x
1
, x
2
, x
3
) = A
1
(x
1
, f(x
1
),
g(x
1
))= B
1
(x
1
) so that the integral I
1
becomes well dened. Therefore, in general, a line integral is
a path-dependent integral. However
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Publisher Resources

ISBN: 9781466569980