Eye of the Storm
I Be-leaf in U
Noah’s Arc Found ?
Let’s Go Fly a Kite !
Tracks at Indy Motor Speedway

A Gift That Keeps On Giving

We see from “Seek-Lock-Strike!” Again that given the missile’s position
where and
are themselves functions of time
It means
That is, let
We also have (see “Seek-Lock-Strike!”)
Since
Substitute (2) into (1) yields
It follows that , the position of the missile satisfies the initial-value problem
To obtain the missile’s trajectory, we solve (4) numerically using the Runge-Kutta algorithm. It integrates (4) from to
(see “Seek-Lock-Strike!”).
Fig. 1
The missile strike is illustrated in Fig. 1 and 2.

Fig. 2

Fig. 3
The trajectories shown are much smoother than those in “Seek-Lock-Strike!” Animated.
“Seek-Lock-Strike!” Animated

In “Seek-Lock-Strike!” Again, we obtained the missile’s trajectory. Namely,
where
Since the fighter jet maintains its altitude (), the missile must strike it at
. Setting
in
gives
Hence, we can plot
Fig. 1
We can also illustrate “Seek-Lock-Strike” in animations:
Fig. 2
Fig. 3
“Seek-Lock-Strike!” Again

We can derive a different governing equation for the missile in “Seek-Lock-Strike!“.

Fig. 1
Looking from a different viewpoint (Fig. 1), we see
Solving (1) for ,
We also have
Equate (1) and (2) gives
The governing eqaution emerges after differentiate (4) with respect to
We let so
and express (5) as
where

Fig. 2
Using Omega CAS Explorer, we compute the missile’s striking time (see Fig. 3). It agrees with the result obtained previously.

Fig. 3
Exercise-1 Obtain the missile’s trajectory from (*).
“Seek-Lock-Strike!” Simplified

There is an easier way to derive the governing equation ((5), “Seek-Lock-Strike!“) for the missile.
Solving
for we have
From
we also have
Equate (1) and (2) gives
Differentiate (3) with repect to we obtain
(see Fig. 1)

Fig. 1
Let (4) bcomes
Since , dividing
through yields
the governing equation for the missile.