Table 1.

Air combat state.

State	Symbol	Formula
Yaw angle	ψ	$\psi =\psi +\int \frac{g}{vcos\gamma }{n}_{z}sin\mu \text{ dt}$
Pitch angle	γ	$\gamma ={\gamma }_0+\int \frac{g}{v}(n_{z}cos\mu -cos\gamma )\text{ dt}$
Velocity	v	v = v0+∫g(nx−sinγ)dt
Altitude	z	z = z0+∫vsinγdt
Distance between the two sides	d	d = ||r1−r2||
Launch missile	f 1	0 or 1
Yaw angle of missile	ψ1	${\psi }_m={\psi }_{m0}+\int \frac{n_{mc}g}{v_{m}cos{\gamma }_m}\text{dt}$
Pitch angle of missile	γ1	${\gamma }_m={\gamma }_{m0}\mathrm{\text{+}}\int \frac{n_{mh}g}{v_m}-\frac{gcos{\gamma }_m}{v_m}\mathrm{\text{dt}}$
Distance between the missile and the other side	d 1	d = ||rm1−r2||
Heading crossing angle	β	$\beta =arccos(\frac{v_1·v_2}{\left|\right|v_1\left|\right|\left|\right|v_2\left|\right|})$
Launch missile of the other side	f 2	0 or 1