数模第四次作业

f=sym('-0.2*x+120*exp(-0.6*t)');
a=0; b=20; h=0.4;
n=(b-a)/h+1; % n=(b-a)/h;
t=0; x=0;
szj=[t,x];
for i=1:n-1 % i=1:n
l1=subs(f,{'t','x'},{t,x});
l2=subs(f,{'t','x'},{t+h/2,x+l1*h/2});
l3=subs(f,{'t','x'},{t+h/2,x+l2*h/2});
l4=subs(f,{'t','x'},{t+h,x+l3*h});
x=x+h*(l1+2*l2+2*l3+l4)/6;
t=t+h;
szj=[szj;t,x];
End
szj
plot(szj(:,1),szj(:,2), 'dg-')
szj =
0 0
0.4000 40.9465
0.8000 70.0080
1.2000 89.9626
1.6000 10
2.9767
2.0000 110.7376
2.4000 114.5566
2.8000 115.4504
3.2000 11
4.2055
3.6000 111.4280
4.0000 107.5832
4.4000 103.0264
4.8000 98.0273
5.2000 92.7892
5.6000 87.4633
6.0000 82.1611
6.4000 76.9630
6.8000 71.9259
7.2000 67.0883
7.6000 62.4749
8.0000 58.1000
8.4000 53.9700
8.8000 50.0857
9.2000 46.4434
9.6000 43.0367
10.0000 39.8569 10.4000 36.8941
10.8000 34.1374
11.2000 31.5756
11.6000 29.1973
12.0000 26.9914 12.4000 24.9468
12.8000 23.0528
13.2000 21.2994
13.6000 19.6767
14.0000 18.1756 14.4000 16.7874
14.8000 15.5039
15.2000 14.3176
15.6000 13.2213
16.0000 12.2083 16.4000 11.2725
16.8000 10.4080
17.2000 9.6095
17.6000 8.8721
18.0000 8.1910 18.4000 7.5621
18.8000 6.9813
19.2000 6.4451
19.6000 5.9500
20.0000 5.4928
=
17
v/
m
s
（3）如图所示
（4）MATLAB程序
a=8;
dogxa=[];rabbitxa=[];dogya=[];rabbitya=[];
d=1;
dogx=-100*sqrt(2);dogy=-100*sqrt(2);rabbitx=0;rabbity=0;
t=0;
dt=0.01;
for b=8:0.5:40
dogx=-100*sqrt(2);dogy=-100*sqrt(2);rabbitx=0;rabbity=0;
t=0;
c=b;
a=8;
while(sqrt((dogx-rabbitx)^2+(dogy-
rabbity)^2)>d&rabbity<60*sqrt(2))
%while cabbity<60*sqrt(2)
if(sqrt((dogx-rabbitx)^2+(dogy-rabbity)^2)<=30)
b=b*1.1^dt;
a=a*0.5^dt;
end
t=t+dt;
d ogx=dogx+b*dt*(rabbitx-dogx)/sqrt((dogx-rabbitx)^2+(dogy-rabbity)^2);
d ogy=dogy+b*dt*(rabbity-dogy)/sqrt((dogx-rabbitx)^2+(dogy-rabbity)^2);
r abbitx=rabbitx-a*dt*cos(pi/4);
r abbity=rabbity+a*sin(pi/4)*dt;
end
if (rabbity<=60*sqrt(2))
b=c;
b reak
end
end
fprintf('the minspeed of dog is:%2f',b);
a=8;
b=15.5;
dogxb=[];rabbitxb=[];dogyb=[];rabbityb=[];
dogx=-100*sqrt(2);dogy=-100*sqrt(2);rabbitx=0;rabbity=0; t=0;
dt=0.01;
s=0;
while(sqrt((dogx-rabbitx)^2+(dogy-rabbity)^2)>d)
t=t+dt;
if(sqrt((dogx-rabbitx)^2+(dogy-rabbity)^2)<=30)
b=b*1.1^dt;
a=a*0.5^dt
end
dogx0=dogx;
dogy0=dogy;
dogx=dogx+b*dt*(rabbitx-dogx)/sqrt((rabbitx-dogx)^2+(rabbity-dogy)^2);
dogxb=[dogxb,dogx];
dogy=dogy+b*dt*(rabbity-dogy)/sqrt((rabbitx-dogx)^2+(rabbity-dogy)^2);
dogyb=[dogyb,dogy];
rabbitx=rabbitx-a*dt*cos(pi/4);
rabbity=rabbity+a*sin(pi/4)*dt;
rabbitxb=[rabbitxb,rabbitx];
cabbityb=[cabbityb,cabbity];
s=s+sqrt((dogx0-dogx)^2+(dogy0-dogy)^2);
end
fprintf('the length dog run is:%.1f',s);
plot(dogxb,dogyb,rabbitxb,rabbityb,'*')。