Ballistics, 2nd Edition

263Trajectories

We can now write the three equations of motion with x as the independent variable as follows:

′

==−













−V

V

VC

V

V

VW

x

x

x

x

xx

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

VW

z

x

z

x

zz

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 ...