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Dynamics of a controlled anti-aircraft missile...
The launcher is a perfectly stiff body with mass mv, moments of inertia Ivx, Ivy and Ivz and a moment of deviation Ivxz- The launcher is mounted on the yehicle using four passive elastic-attenuating elements with linear pa-rameters kv\\ and cvn, kvi2 and 0^12, kv\3 and cv 13 as well as kv 14 and cv 14, respectively.
The turret is a perfectly stiff body with mass mw and main central moments of inertia Iw^v, Iwr\'v-> ^wC'v- The guide raił is also a perfectly stiff body with mass mpr and main central moments of inertia Ipr^, Iprrjpv ■, Iprępv ■
If the basie motion of the launcher is not disturbed, then the 0vxvyvzv, Svxvyvzv and Sv£vrjvęv coordinate systems coincide at any moment. The turret model as an element of the spatially vibrating system performs complex motion with respect to the 0vxvyvzv reference system consisting of straightline motion of the mass centre Sv, in accordance with a change in the yv coordinate, rotary motion about the Svzv axis in accordance with a change in the pitch angle and rotary motion about the Svxv axis in accordance with a change in the tilt angle tpv.
Prior to the launch, the missile is rigidly connected with the guide raił. The mounting prevents the missile from moving along the guide raił. Once the missile motor is activated, the missile moves along the raił.
The guide rail-missile system used in the analysis ensures collinearity of points on the missile and the guide raił.
It is assumed that the longitudinal axis of the missile coincides with the longitudinal axis of the guide raił at any moment and that the missile is a stiff body with an unchangeable characteristic of inertia. The missile is a perfectly stiff body with mass mp and main central moments of inertia IpXp, Ipyp, IpZp-The geometrie characteristic of the guide rail-missile system shown in Fig. 2a and Fig. 2b can be used to analyze the dynamics of the controlled system.
The main view of the turret-missile system model is presented in Fig. 2a. It includes an instantaneous position of the missile while it moves along the guide raił. Figurę 2b shows the top view of the turret-missile system model. It includes the instantaneous position of the missile while it moves along the guide raił.
The missile model performs straightline motion with respect to the Sv^pvf1pvCpv reference system according to a change in the coordinate.
The model of the launcher-missile system has six degrees of freedom, which results from the structure of the formulated model. The positions of the system were determined at any moment assuming four independent generalized coordinates:
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