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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
233Trajectories
But because we are in an inertial frame, i
= j
= k
= 0 and therefore
d
d
V
ijk
t
VVV
xyz
=++

(8.50)
If we break Equation 8.47 into its components, we get three coupled, ordinary, nonlinear
differential equations
VCVV
xx
=
ˆ
D
*
(8.51)
VCVV g
yy
=−
ˆ
D
*
(8.52)
VCVV
zz
=
ˆ
D
*
(8.53)
The equation that couples Equations 8.51 through 8.53 is
V
VVV
xyz
=++
222
(8.54)
We can linearize these equations by making a few assumptions. First, let us assume that
there is no crosswind, so V
z
= 0, and if we further constrain the ratio of the vertical velocity
to the horizontal velocity to |V
y
/V
x
| = tan ϕ < 0.1, then V and V
x
are within 0.5% of each
other, and w
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Publisher Resources

ISBN: 9781466564374