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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
140 Classical Mechanics
© 2010 Taylor & Francis Group, LLC
Hence,
pPQq
PQ==
4
µµ
co
s/
sin, . (5.38)
Now, we can evaluate the new Hamiltonian K. Because the generating function F
1
does not
depend on time explicitly, we have
KH
m
pkq
kP
Q
mk
Q
== +
=+
1
2
1
2
2
4
22
2
2
2
µ
µ
si
nc
os
.
If
µ= mk
/2
, this reduces to
KkPP
km
==
//
2µ
(5.39)
which is of a particularly simple form. Because the new coordinate Q is a cyclic coordinate, the
new momentum P conjugated to Q is a constant of the motion:
PKQ=−∂∂=
/0
and
P = β (a constant of the motion). (5.40)
Hamilton’s equations of motion for the new coordinate Q gives
QK
Pk
m=∂ ∂=
//
from which we obtain
Qkmt
=+
/ α
(5.41)
where α is the ...
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Publisher Resources

ISBN: 9781466569980