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军事模型(数学建模)

发布时间:2020-05-23 09:15:51 已有: 人阅读

        Mathematic Modeling                                           Lanchester    ...

        Mathematic Modeling                                           Lanchester              1.   2. 3.               Lanchester              1.   2. 3.               Lanchester              1.   2. 3.               Lanchester                              Lanchester            x  y  x  y  f x = f(y)    x  x0   x0  y = g(x)    M  xm ym   x f(y)              Lanchester            x  y  x  y  f x = f(y)    x  x0   x0  y = g(x)    M  xm ym   x f(y)              Lanchester         Oxxmx0yymy0MMM             Lanchester             x = f(y) y = g(x)              Lanchester          r   y = rx   y   p(r) r  p(r) 0  xp(r)  xp(r)  x0   xp(r)  x0 x  r  xr   xr x = f(y)  y = rx   r  x = f(y)  y = rx   r  y = g(x)  x = ry  y = g(x)  xr x = f(y)             Lanchester             p(r)   f(y)   x0    M     y0 g(x)                 Lanchester            N   x0/N   x = f(y)   N   g(x)              Lanchester         Oxxmx0yymy0Ax0/NB             Lanchester         Lanchester Lanchester                              Lanchester          x(t)  y(t)  t   1.   f(x, y)  g(x, y) 2.    3.   u(t)  v(t)              Lanchester          x(t), y(t) ˙ x(t)˙ y(t)==f(x, y) x + u(t),g(x, y) y + v(t), 0 0(1)  f g               Lanchester          x(t), y(t) ˙ x(t)˙ y(t)==f(x, y) x + u(t),g(x, y) y + v(t), 0 0(1)  f g               Lanchester           f(x, y).      f  y  f = ay a   a  a = rypy  ry)py             Lanchester           f(x, y).      f  y  f = ay a   a  a = rypy  ry)py             Lanchester          g = bx  b = rxpx rx px˙ x(t)=ay x + u(t)˙ y(t)=(1)bx y + v(t)(2)             Lanchester              x0 y0 (2)˙ x˙ y===aybxx0,x(0)y(0) = y0(3)             Lanchester         (3)  (3)dydx=bxay(4)ay2 bx2= k(5)(3) k = ay20 bx20(6)             Lanchester         (3)  (3)dydx=bxay(4)ay2 bx2= k(5)(3) k = ay20 bx20(6)             Lanchester         (3)  (3)dydx=bxay(4)ay2 bx2= k(5)(3) k = ay20 bx20(6)             Lanchester         (5)   t x(t) y(t)   k 0  y t1,x(t1) = 0,y(t1) =   k 0   k = 0 ka 0, :              Lanchester         (5)   t x(t) y(t)   k 0  y t1,x(t1) = 0,y(t1) =   k 0   k = 0 ka 0, :              Lanchester          (6) a b  y0x02ba=rxpxrypy(7)             Lanchester         (7) y0/x0 2    4  rx 4 px ry py   y0 2                Lanchester          sx        f = cxy  c  c = rypy= ry ry  py sry sxsrysx             Lanchester          sx        f = cxy  c  c = rypy= ry ry  py sry sxsrysx             Lanchester         g = dxy d = rxpx= rxsrx(1)˙ x(t)˙ y(t)sy. ==cxy x + u(t)dxy y + v(t)(8)             Lanchester          x  y  u = v = 0 (8)˙ x˙ y===cxydxyx0,x(0)y(0) = y0(9)             Lanchester         (3) (9)cy dx = m(10)m = cy0 dx0(11)(10)    m 0  m 0  m = 0              Lanchester         Ox(t)y(t)m = 0, m 0, m/dm/cm 0, :              Lanchester         y0x0dc=rxsrxsxrysrysy(12) y0/x0  s  y0              Lanchester           f = cxy g = bx  ˙ x˙ y===cxybxx0,x(0)y(0) = y0(13)             Lanchester           f = cxy g = bx  ˙ x˙ y===cxybxx0,x(0)y(0) = y0(13)             Lanchester         cy2 2bx = nn = cy20 2bx0(14)(15) :              Lanchester         cy2 2bx = nn = cy20 2bx0(14)(15) :              Lanchester          n 0  n 0  n = 0  y0x022bcx0(16) b = rxpx c = rysrysxy0x022rxpxsxrysryx0(17)             Lanchester            x0= 100  px= 0.1  rx ry  sx= 0.1  sry= 1  (17)(17)y0x022 0.1 0.1 × 1062 1 100= 100(18) y0/x0 10  10              Lanchester                8  6                Lanchester         J H Engel   :              Lanchester         J H Engel   :              Lanchester         Richardson, 1939  1.     2.     3.                 Lanchester         Richardson, 1939  1.     2.     3.                 Lanchester           x(t), y(t) 1. x(t)  y(t) 2. x(t)  x(t) 3.  x(t) ˙ x˙ y==x + ky + glx y + h(19)(k, l, , , g, h  0)             Lanchester           x(t), y(t) 1. x(t)  y(t) 2. x(t)  x(t) 3.  x(t) ˙ x˙ y==x + ky + glx y + h(19)(k, l, , , g, h  0)             Lanchester         x + ky + glx y + h==00(20)             Lanchester         1         (19) (19)  k  l   g  h   g, h  k, l              Lanchester         1         (19) (19)  k  l   g  h   g, h  k, l              Lanchester         2   g = h = 0    x(t) = y(t) = 0 (19)  x(t), y(t) 3 g, h  = 0  x(t), y(t)  ˙ y = h, x(t), y(t) ˙ x = g,4  x(t) = 0  g = 0  ˙ x = ky x(t)              Lanchester         2   g = h = 0    x(t) = y(t) = 0 (19)  x(t), y(t) 3 g, h  = 0  x(t), y(t)  ˙ y = h, x(t), y(t) ˙ x = g,4  x(t) = 0  g = 0  ˙ x = ky x(t)              Lanchester         2   g = h = 0    x(t) = y(t) = 0 (19)  x(t), y(t) 3 g, h  = 0  x(t), y(t)  ˙ y = h, x(t), y(t) ˙ x = g,4  x(t) = 0  g = 0  ˙ x = ky x(t)              Lanchester         (19)˙X = AX + R  A               Lanchester         (19)˙X = AX + R  A               Lanchester          kl  = 0  (19) =( + ) [( + )2 4( kl)]1/22=( + ) [( )2+ 4kl]1/22   kl 0    (x0, y0)  kl 0   (x0, y0)              Lanchester          kl  = 0  (19) =( + ) [( + )2 4( kl)]1/22=( + ) [( )2+ 4kl]1/22   kl 0    (x0, y0)  kl 0   (x0, y0)              Lanchester          kl 0  (x0, y0)   kl(21)(21)    (21)  , , k, l.  Richardson              Lanchester          kl 0  (x0, y0)   kl(21)(21)    (21)  , , k, l.  Richardson              Lanchester          g = 0, y = y1  x = 0 ˙ x = ky1 1k=y1˙ x(22)(22) y11k             Lanchester             19331936    1k= 3   k.= 0.3.             Lanchester          .  g = 0, y = 0 (19) ˙ x = x x(t) = x(t0) e(tt0)x(t0+1) = x(t0) e1(23)(23)e  Richardson   = 0.2 111      

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