It’s a mathematical model of an Air Defense System intercepting an unguided ballistic target, complete with an animated XY-plot.

Here is a quick overview of the math and physics inside the model:

- The Target (Blue trace): Modeled as a projectile launched at 700 m/s at a 60° angle. Its flight is governed by 2nd-order ODEs accounting for gravity and aerodynamic drag (using an exponential air density model based on altitude).
- The Missile (Red trace): Launched from a distance of 15 km with a constant speed of 350 m/s. It uses a continuous "Pure Pursuit" guidance law, meaning its velocity vector is constantly updated in the ODE to point directly at the target's current coordinates.
- The Core Logic: Instead of calculating the trajectories separately or using discrete loops, both the target's physics and the missile's guidance logic are unified into a single system of differential equations. The entire engagement is solved simultaneously using the built-in rkfixed solver.
- Launch Delay: The missile equations include a launch delay condition (t0​ = 8 s) so the missile waits for the target to enter the optimal engagement zone.

I've attached the .sm document along with a GIF animation of the result.

You can play around with the launch delay (t.0), missile speed (v.r), or launch angle to see how the interception trajectory changes.



air-defense.sm (26,84 KiB) descargado 706 vez(es).
air-defense.pdf (86,6 KiB) descargado 509 vez(es).

You can learn about the problem and its solution from the article​
V.F. OCHKOV, I.E. VASILEVA
APPLICATION OF DIFFERENCE SCHEMES TO DECISION THE PURSUIT PROBLEM
https://ia.spcras.ru/index.php/sp/article/view/4041/2619