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Ballistics, 2nd Edition
book

Ballistics, 2nd Edition

by Donald E. Carlucci, Sidney S. Jacobson
August 2013
Intermediate to advanced content levelIntermediate to advanced
608 pages
21h 36m
English
CRC Press
Content preview from Ballistics, 2nd Edition
464 Ballistics: Theory and Design of Guns and Ammunition
If we write the force balance in the x-direction, we obtain
ρ
τ
fxyz yz
x
xy
zy
z
xz
xxx
xx
xx
yx
()() ()
()
()
dddddddd dd
dd
++
++
σσ
σσ
σσ
ττ
τ
yx
yx x
y
yxzxzxyzu
−=dddddddd()()
()
ρρ

(16.171)
After we cancel terms and divide by the volume dxdydz, we obtain
ρ
σ
τ
ρ
f
xy
u
x
xx
yx
x
+
+
=

(16.172)
Examined in three dimensions, the equation would be
ρ
σ
τ
τ
ρρ
f
xyz
uf
x
u
x
xx
yx
zx
xi
ij
j
i
+
+
+
=→+
=
 
σσ
ρ
(16.173)
If we recall Hooke’s law in its one-dimensional form, we get
σε
= E
(16.174)
In three dimensions, it is written for a homogeneous material using two material con-
stants, called the Lamé constants, as
σλεµε
ij kk ij ...
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Publisher Resources

ISBN: 9781466564374