弹道龙格库塔法

利用常微分方程的龙格库塔法解算弹道，并进行弹道优化，得到最优参数

clc;
clear;
m0=15800;
mp=12912;
tall=115;%发动机点火时间
P=260680;
mu=3.986004e14;
R=6378.14e3;
t1=3;
t2=20;%经估算，加速40s后，导弹速度约为0.8Ma
alp=-1/57.3;
c=-mp/tall;%秒耗量
tout=[];
yout=[];
r=[];
height=[];
yout（1:）=[0 0 0 0 m0];
i=1;
h=0.1;
for t=0:h:1000
    tout（i1）=t;
    r（i1）=sqrt（yout（i1）^2+（R+yout（i2））^2）;
    height（i1）=r（i1）-R;
    gr=-mu/（r（i1）^2）;
   
    if t>2
       if height（i1）<10
          break
        end
    end

    if t>0
        the=atan（yout（i4）/yout（i3））;
    end
    
    if t<3
        phi=90/57.3;
    elseif t<20
        phi=the+alp;
    elseif t<115
        phi=the;
    else
        phi=the; 
        c=0; 
        P=0;
    end
    
    K1m=h*c;
    K2m=h*c;
    K3m=h*c;
    K4m=h*c;
    
    K1x=h*yout（i3）;
    K2x=h*（yout（i3）+K1x/2）;
    K3x=h*（yout（i3）+K2x/2）;
    K4x=h*（yout（i3）+K3x）;
    
    K1y=h*yout（i4）;
    K2y=h*（yout（i4）+K1y/2）;
    K3y=h*（yout（i4）+K2y/2）;
    K4y=h*（yout（i4）+K3y）; 
    
    K1vx=h*（P/yout（i5）*cos（phi）+gr/r（i1）*yout（i1））;
    K2vx=h*（P/（yout（i5）+K1m/2）*cos（phi）+gr/r（i1）*（yout（i1）+K1x/2））;
    K3vx=h*（P/（yout（i5）+K2m/2）*cos（phi）+gr/r（i1）*（yout（i1）+K2x/2））;
    K4vx=h*（P/（yout（i5）+K3m）*cos（phi）+gr/r（i1）*（yout（i1）+K3x））;
    
    K1vy=h*（P/yout（i5）*sin（phi）+gr/r（i1）*（R+yout（i2）））;
    K2vy=h*（P/（yout（i5）+K1m/2）*sin（phi）+gr/r（i1）*（R+yout（i2）+K1y/2））;
    K3vy=h*（P/（yout（i5）+K2m/2）*sin（phi）+gr/r（i1）*（R+yout（i2）+K2y/2））;
    K4vy=h*（P/（yout（i5）+K3m）*sin（phi）+gr/r（i1）*（R+yout（i2）+K3y））;  
    
    yout（i+11）=yout（i1）+1/6*（K1x+2*K2x+2*K3x+K4x）;
    yout（i+12）=yout（i2）+1/6*（K1y+2*K2y+2*K3y+K4y）;
    yout（i+13）=yout（i3）+1/6*（K1vx+2*K2vx+2*K3vx+K4vx）;
    yout（i+14）=yout（i4）+1/6*（K1vy+2*K2vy+2*K3vy+K4vy）;
    yout（i+15）=yout（i5）+1/6*（K1m+2*K2m+2*K3m+K4m）;
    i=i+1;
end

figure（1）;
plot（yout（:1）/1000yout（:2）/1000）;
grid on;
title（‘导弹在发射坐标系下的轨迹‘）;
xlabel（‘x/km‘）;ylabel（‘y/km‘）;
        
  

 属性            大小     日期    时间   名称
----------- ---------  ---------- -----  ----
     文件        2025  2012-12-20 10:32  弹道Runge-Kutta法\RungeKuttamain.m
     文件        1943  2012-12-20 10:32  弹道Runge-Kutta法\zhudong.m
     目录           0  2013-03-03 11:20  弹道Runge-Kutta法\