中南数学建模作业

1.(1)(x)=x2 s i n(x2 x 2),-2 x ,X Zelf;x=0:0.125:2*pi;yl=cos(x);y2=sin(x-pi/2);y3=x.A2.*cos(x-pi);y4=exp(sin(x);subplot(2,2,l);plot(x,yl);title(cos(x);grid onsubplot(2,2,2);plot(x,y2);title(,sin(x-pi/2);grid onsubplot(2,273);plot(x,y3);title(x.八 2.*cos(x-pi);grid onsubplot(2,2,4);plot(x,y4);title(,exp(sin(x),);grid onsin(x-pi/2)2作出极坐标方程为r=2(l-cosf)的曲线的图形.e l f;t =0:0.0 1:2*p i;p o l a r(t,2*(1-c o s(t)9043作出极坐标方程为r=e的对数螺线的图形.elf;t=linspace(0,6*pi);polar(t,exp(t/10)270 x=4cos4绘制螺旋线1y=4siin,在 区 间0,4%上的图形,在上实验中，显示坐标轴名称。z=telf;t=0:0.125:4*pi;x=4*cos(t);y=4*sin(t);z=t;plot3(xf y,z);grid onxlabel(x);ylabel(y1);zlabel(z);5作出函数2=-XW”4的图形.elf;x=-3:0.1:3;y=x;xz y=meshgrid(x,y);z=-x.*y.*exp(-x.A2-y.A2);mesh(x,y,z)xlabel(x1);ylabel(y);zlabel(z1);6作出椭球面上+匚=1的图形.4 9 1(该曲面的参数方程为 x=2sin wcosv,y=3sin u sin v,z=cosw,(0 w 凡0 v 2).)e lf;u=linspace(0,pi);v=linspace(0,2*pi);u,v=meshgrid(u,v);x=2*sin(u).*cos(v);y=3*sin(u).*sin(v);z=cos(u);mesh(x,yz z);grid onxlabel(x1);ylabel(1y);zlabel(z 1);-0.5yx2 2 27 作双叶双曲面 J+J-J=-l 的图形.1.52 1.42 1.32(曲面的参数方程是 x=1.5 cot“cos v,y=1.4cotwsin v,z=1.3cscw,其中参数0 4%，-乃 ”T 时对应双叶双曲面的一叶，参数4 0,-乃 v 乃时对应2 2双叶双曲面的另一叶.)elf;uz v=meshgrid(linspace(-pi/2,pi/2)zlinspace(-pi,pi);x=l.5*cot(u).*cos(v);y=l.4*cot(u).*sin(v)；z=l3*csc(u);mesh(x,yz z)xlabel(1x1);ylabel(1y1);zlabel(z);8 作出圆环 x=(8 +3cosv)cos,y=(8 +3cosu)sin,z=7 sin u,(0 4 W 3乃/2,/2 v3-34盯=0)1 +/2 1 +r2elf;t=-10:0.1:10;a=l;xl=3*a*t./(1+t.A3);yl=3*a*t.2./(1+t.A3);plot(xl,yl);grid onxlabel(1x1);ylabel(y);102 3 314.蔓叶线x=鼻,y=鼻(/=-)1 +r 1 +r a-xelf;t=linspace(-4,4);a=l;x=a*t.A2./(l+t.A2);y=a*t,A3./(l+t.A2);plot(x,y);grid on;xlabel(x);ylabel(y);4/z一_一一r.s_ _、0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x15.摆线 x=a(t-s in t y =b(l-cost)elf；t=linspace(-2*piz 2*pi);a=l;x=a*(t-sin(t);y=a*(1-cos(t);plot(x,y);grid on;xlabel(x);ylabel(y);2 2 21 6.内 摆 线(星 形 线)x=6 zc os3 t,y=4 zs i n31(+y，=)elf;t=linspace(-pi,pi);a=l；x=a*cos(t).人3;y=a*sin(t).人3;plot(x,y);grid on;xlabel(x);ylabel(1y1);17.圆的渐伸线(渐开线)x=a(cos，+fsinty =tz(sinr-rcosf)elf；t=linspace(-pi,pi);a=l;x=a*(cos(t)+t.*sin(t);y=a*(sin(t)-t.*cos(t);plot(x,y);grid on;xlabel(x);ylabel(y*);418.空间螺线 x=a cos t,y=b sin t.z=ctelf；t=linspace(0,5*pi);a=l;x=cos(t);y=2*sin(t);z=3*t;plot3(xz y,z);grid on;xlabel(x);ylabel(y);zlabel(z);19.阿基米德线r=a(p,r 0 oelf；t=linspace(0,6*pi);a=2;r=a*t;polar(t,r)0270_ a cp20.对数 螺 线丫=eelf;t=linspace(-2*pi,0);a=l;r=exp(a*t);polar(3 r);21.双纽线r?=a cos2(p(x2+y2)2=a2(x2-y2)elf;p=0:0.01:2*pi;a=l;r=a*sqrt(cos(2*p);polar(p,r);X22.双纽线r?=a sin2(p(x2+y2)2=2a2xy)elf;p=0:0.01:2*pi;a=l;r=a*sqrt(sin(2*p);polar(p,r);23.四叶玫瑰线r=a sin 2(p j 0elf;t=linspace(0,2*pi);a=l;r=a*sin(2*t);polar(t,r);27024.玫瑰线 r-a sin 3(p,r 0elf;t=linspace(0,2*pi);a=2;r=a*sin(3*t);polar(t,r);027025.三叶玫瑰线r=tzcos3,r 0elf;t=linspace(0,2*pi);a=2;r=a*cos(3*t);polar(tz r);290027026.作出以参数方程表示的空间曲线X=二co s-r,y=-e-Q-2t sin=0,202.2elf;t=linspace(0,20);x=exp(-0.2*t).*cos(pi/2)*t);y=(pi/2)*exp(-0.2*t).*sin(t);z=t;plot3(x,y,z);xlabel(x);ylabel(y);zlabel(z1);grid on20181614121086420227.以绘制极坐标系下曲线P=Q C O SS+6),并讨论参数。力,的影响。elf;t=linspace(0,2*pi);a=l;b=pi/3;n=2;r=a*cos(b+n*t);polar(t,r);讨论：a 控制叶的长；-b为其中一个叶与极轴的夹角；n为奇数时，页数为n,n为偶数时，页数为2n；2 8.(曲线族绘制)三次抛物线的方程为y=a/+c x,试探讨参数a和c对其图形的影响。elf;t=linspace(0,10);a=l;c=10;y=a*t.A3+c*t;plot(tz y);xlabel(x);ylabel(y);grid on讨论：a和c同样是改变函数幅值，但a对其影响较大29.做 出 卜列函数的图像：(1)y(x)=x2 sin(x2-x-2),-2 x 2(分别用 plot、fplot)if;syms xfplot(fxA2*sin(xA2-x-2)1,-2 2)grid on;xlabel(x*)；ylabel(y*);3elf;x=-2:0.01:2;y=x.A2.*sin(x.A2-x-2);plot(x,y)grid onxlabel(1x*);ylabel(y);(2)x2/4+y2/16=l(用参数方程)elf;t=0:0.125:2*pi;x=2*sin(t);y=4*cos(t);plot(xz y);xlabel(x1);ylabel(y);grid on(3)在同一图形窗口中，画出四幅不同图形(用s u b p l ot 命令)：见题一(3)；3 0.画出空间曲线z=在一3 0 x,y 3 0 范围内的图形，并画出相应的等J l+/+y 2高线。elf;x,y=meshgrid(-30:0.1:30);z=10.*sin(sqrt(x.A2+y.A2)./sqrt(1+x.A2+y.A2);mesh(x,y,z);xlabel(x1)z ylabel(y)z zlabel(z);grid on;6、elf;xz y=meshgrid(-30:0.1:30);z=10.*sin(sqrt(x.A2+y.A2)./sqrt(1+x.人2+y A2);contour3(x,y,z,12,1k1);xlabel(x1),ylabel(y),zlabel(1z1);grid on;-r631.根据给定的参数方程，绘制下列曲面的图形。a)椭球面 x=3 cos u sin v,y=2cos M cos v,z=sin welf;uz v=meshgrid(linspace(0,2*pi),linspace(0,pi);x=3*cos(u).*sin(v);y=2*cos(u).*cos(v);z=sin(u);mesh(x,y,z)xlabel(1x*);ylabel(*y1);zlabel(*z*b)椭圆抛物面 x=3u sin v,y=2wcosv,z=4w218 elf；1 9.u,v=meshgrid(linspace(-2*pi,2*pi),linspace(Oz 2*pi);2 0.x=3*u.*sin(v);2 1 .y=2*u.*cos(v);22 z=4*u.人2;2 3 .mesh(x,y,z)2 4.xlabel(f x*);ylabel(*y*);zlabel(*z1);e)uz v=meshgrid(linspace(-2*pi,2*pi)rlinspace(Oz 2*pi)；f)x=3*sec(u).*sin(v);g)y=2*sec(u).*cos(v);h)z=4*tan(u);i)mesh(x,y,z);j)xlabel()；ylabel(1y1);zlabel(1 z*)；a)双曲抛物面x=，y=v,z=-3k)elf;1)u,v=meshgrid(linspace(-5*pi,5*pi),linspace(-5*piz 5*pi);m)x=u;n)y=v;O)z=(u.A2-v.A2)/3;p)mesh(x,y,z);q)xlabel(*x);ylabel(*y*);zlabel(1z*);a)旋转面x=I n ws i n v,y=I n wc os匕 z=r)elf；S)u,v=meshgrid(linspace(0,5*pi),linspace(-5*piz 5*pi);t)x=log(u).*sin(v);u)y=log(u).*cos(v);v)z=u;w)mesh(xz yz z);X)xlabel(1x);ylabel(1y1);zlabel(1z*);20-a)圆锥面 x=u sin v,y=u cos v,z=uy)elf;z)u,v=meshgrid(linspace(-5*pi,5*pi),linspace(-5*piz 5*pi);a a)x=u.*sin(v);b b)y=