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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
592 Appendix 2
and from Equation 4.1, we nd
dddand d

r
r
q
q
r
t
tr
r
q
q
i
i
j
j
j
n
i
i
i
j
=
+
=
=
1
jj
j
n
i
r
t
=
+
1
. (A2.20)
The partial derivatives in Equation A2.20 are themselves functions of the generalized coordinates q
i
and the time. As a result, the particle velocities have the following functional form:

rrqqqqi
ii nn
==
(,..., ;,..., ),,...,
11
1
,2
NN.
Moreover, Equation A2.20 provides an explicit function of the indicated variables and shows that
r
i
in fact depends linearly on the generalized velocities
q
j
. Thus, we can readily evaluate the partial
derivative
∂∂
rq
ij
/
to obtain
∂∂ =∂
rq
rq
ij
ij
//
. (A2.21)
Note that now the independent ...
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Publisher Resources

ISBN: 9781466569980