[[theta].sub.M] is the flight-path angle of the interceptor.
The initial flight-path angle is [[theta].sub.T0] = 0 deg.
The initial position of the interceptor is set as [x.sub.M0] = 0 m and [y.sub.M0] = 0 m, and the initial flight-path angle is [[theta].sub.M0] = 30 deg.
Velocity parameters of HGV are described by velocity magnitude V, heading angle [theta], and flight-path angle [sigma].
The initial states (reentry points parameters) are taken as follows: geocentric distance [r.sub.0] = [R.sub.0] + 79.248 km ([R.sub.0] is Earth radius), longitude [[lambda].sub.0] = 0[degrees], latitude [[phi].sub.0] = 0[degrees], velocity [V.sub.0] = 6278.8 m/s, heading angle [[theta].sub.0] = -1[degrees], and flight-path angle [[sigma].sub.0] = 90[degrees].
Firstly, in the altitude loop, the virtual control inputs about flight-path angle and attack angle are designed step by step according to the backstepping strategy.
This model is composed of five rigid-body states, that is, velocity V, altitude h, flight-path angle [gamma], attack angel [alpha], pitch rate q, and six flexible states, that is, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
So the flight-path angle command [[gamma].sub.d] is designed into the following equation:
From the Fig.4 it is clear that bank angle is [phi], the heading angle is X and [gamma] is the flight-path angle
. T is the thrust that is produced by aircraft's engine.
Consequently, the model is objectively complex with a total of 29 equations: 9 fuselage equations, 16 blade flapping and lead-lagging equations, 3 static main-rotor downwash equations, and an additional flight-path angle
As characteristics of the surface-to-surface engagement, the flight-path angle of target equals to [pi] which is under the condition of an incoming target.
If the missile follows PN guidance law with a navigation gain N, the flight-path angle rate can be written as