
312 Ballistics: Theory and Design of Guns and Ammunition
or, using our denition of starred coefcients, we have
d
d
** *
*
YY YY
2
2
2
0
Y
t
V
d
CC C
d
V
C
qd
V
g
q
=++
+
−
αα
α
α
(9.29)
Equation 9.29 can be combined with Equation 9.21 to develop a single equation for projec-
tile motion. With this, the dynamic equation for the pure pitching motion of a projectile
can then be described as
α
+−
(9.30)
This linear, second-order differential equation with constant coefcients was established
by Murphy [1] and modied here (the terms with the “d” subscript) to account for the
assumption of zero drag. In this expression, we identify the ...