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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
67Integration of Newton’s Equation of Motion
© 2010 Taylor & Francis Group, LLC
xt
tt
m
Ft t
t
() ()=
′′
d
0
.
We can rewrite this as
xt GttF
tt
t
() (, )()=
′′
d
0
, (3.24)
where we have dened
G(t,t) = (tt)/m. (3.25)
G(t,t) is called Green’s function for this particular system and is here a function only of the differ-
ence (t – t). The equation for x(t) is an example of an integral equation, G(t,t) being a so-called inte-
gral kernel, which, here, converts the applied force function F(t) into the displacement function x(t).
To complete the above example, we assume that F(t) = F
0
, a constant, for t ≥ 0. Then
xt
tt
m
Ft t
F
m
tt t
F
m
tt
tt
() ()
()
(
=
′′
=− ...
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Publisher Resources

ISBN: 9781466569980