
263Trajectories
We can now write the three equations of motion with x as the independent variable as follows:
′
==−
−V
V
VC
V
V
x
x
x
x
1
ˆ
D
*
(8.170)
′
==−
−−
V
V
VC
V
V
VW
g
V
y
x
y
x
yy
x
1
ˆ
D
*
()
(8.171)
′
==−
−V
V
VC
V
V
z
x
z
x
1
ˆ
D
*
(8.172)
As we noted earlier, the vertical component of the wind, W
y
, is usually extremely small and
will be neglected in further treatment. Further, as we mentioned, these equations are impos-
sible to solve in closed form and we must resort to numerical methods for their solution.
Without the restrictions of at re, projectiles red at high angles of departure may
traverse the atmosphere to great altitudes. In ...