Month: February 2023
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.
Happy Valentine’s Day!
“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