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Dynamics of a controlled anti-aircraft missile...

Motion of the controlled launcher mounted on a moveable base can be illustrated by means of the following eąuations

d_v =    {hjjy + b₈<fv + W(_pv + bi₀ii>_pv + bwd_pv)] + M#

07

\Pv = 7—[^z3 ~ {bzVv + bs$_v + bi3^_pv + 614^pv + bisti_pv)\ +

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Vv = tI^z1 - (Mt, + b₃lfi_v + b₄^_pv + hi>pv + Wzw)] + Fy

1    ..    ..    ..    ..    P.i)

iijn) =    ^— (p5Vv +    + bu(fi_v + 6l7^pw + &20$pu)] +

$pu = 7—[²6 ~ (&62/v +    + frl8łpu + &2oVv)] +

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ipv = 7—[24 - (b₄y_v + bgd_v + bi3<f>_v + btfitpy + &i8^p_V)]

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where

y_v - vertical displacement of the turret mass centre S_v,

<p_v,d_v ~ angle of rotation of the turret about the S_vx_v and S_vz_v axis, respec-tively,

Ępu - straightline displacement of the missile mass centre S_p along the S_v£py axis,

ijj_pv - turret yaw angle,

'dpy - guide raił pitch angle,

- preprogrammed moment of control of the turret pitch angle and the guide raił yaw angle, respectively,

F_y - force stabilizing vertical progressive motion of the launcher,

M$, Mp - moments stabilizing angular motions of the launcher about the S_vz_v and S_vx_v axes,

bi (where i = 1,... ,21) - coordinate functions y_v, d_v, ip_v, ippy, dpy, £py,

Zi (where i = 1,... ,6) - coordinate functions y_v, d_v, ip_v, ijj_pv, 'dpy, £_pv and their derivatives with respect to time y_v, d_v, (p_v, ip_Py, dpy, £_pv.

Explicit forms of the functions bi (y_v ,d_v,tp_v, ippy, d_pv, £_pu) and Zi(2/1?y d_v, vp_v, tjjpy, d_pv, £_pv, y_v, d_v, <p_v, ippy 1 d_pv, ^py) are long mathematical expressions, which developed analytically are available at the authors of the article.