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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
185Motion Under a Central Force
© 2010 Taylor & Francis Group, LLC
or because f(r) = −μg(r)
3
0
ρ
ρρ
ff() ()+
< (6.67)
which is identical to Equation 6.62. In particular, if the force law is a power law
f(r) = −cr
n
where c is a positive constant, then the condition for stability reads
ρ
n−1
(3 + n) > 0. (6.68)
In order for the condition 6.68 to hold, n is restricted to values greater than −3. Hence, we con-
clude that, of the central forces of the form −cr
n
, only those for which n > −3 will provide stable
circular orbits. We notice that the inverse square law (n = −2) gives stable circular orbits as does the
law of direct distance (n = 1). The lat
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Publisher Resources

ISBN: 9781466569980