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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
90 Classical Mechanics
© 2010 Taylor & Francis Group, LLC
Now, all of the indices, i, j, and k are dummies. If we change i to j in the rst term on the right-hand
side and i to k in the second term, then both terms become identical, and we have

q
T
q
aq
qT
i
i
i
n
jk jk
jk
n
==
==
∑∑
11
22
,
.
(4.6)
This is a special case of Euler’s theorem, which states that if f(x
i
) is a homogeneous function of the
x
i
of order n, that is,
f(λx
i
) = λ
n
f(x
i
)
then
x
f
x
nf
i
i
i
=
.
As an illustration of Euler’s theorem, consider the motion of a particle of mass m under the inuence
of a force derived from a potential dependent on position only. The kinetic energy T in Cartesian ...
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Publisher Resources

ISBN: 9781466569980