y=sin(u).*v; z=v;
surf(x,y,z) hold on;
t=0:0.1:2*pi;c=0:0.1:2; [t,c]=meshgrid(t,c); a=1+cos(m); b=sin(m); surf(a,b,c)
11用动画演示由曲线y?sinz,z?[0,?]绕z轴旋转产生旋转曲面的过程. 转所得旋转曲面的方程为x2?y2?sin2z, 其参数方程为
x?sinzcosu,y?sinzsinu,z?z,(z?[0,?],u?[0,2?])）
m=moviein(100); for i=1:100
u=0:0.01:pi/5*(i+0.2); v=0:0.01:pi;
[u,v]=meshgrid(u,v); x=sin(v).*cos(u); y=sin(v).*sin(u); z=v;
mesh(x,y,z)
m(:,i)=getframe; end
movie(m,i);
12. 画出变上限函数?x0tsint2dt及其导函数的图形.
syms t;int('t'.*(sin('t'.^2)),0,'x'); x=-2*pi:0.1:2*pi;y1=x.*sin(x.^2);
y2=-1/2*x.*cos(x).*sin(x)+1/4*x.^2+1/4*sin(x.^2); plot(x,y1,x,y2)
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z轴旋（该曲线绕
13.迪卡尔曲线
3at3at2x?,y?(x3?y3?3axy?0) 221?t1?t
hold on t=0:0.1:4; for a=0:0.1:2;
x=(3.*a.*t)./(1+t.*t); y=(3.*a.*t.*t)./(1+t.*t); plot(x,y); end
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at2at3x3213. 蔓叶线x?,y?(y?) 22a?x1?t1?thold on t=0:1:10;
for a=0:0.5:5;
x=(a.*t.*t)./(1+t.*t); y=(a.*t.*t.*t)./(1+t.*t); plot(x,y); end
14. 摆线x?a(t?sint),y?b(1?cost) a固定时： hold on
a=1; t=0:1:10; for b=0:0.2:2; x=a.*(t-sin(t)); y=b.*(1-cos(t)); plot(x,y); end
b固定时：
hold on
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b=1; t=0:1:5; for a=0:0.5:2; x=a.*(t-sin(t)); y=b.*(1-cos(t)); plot(x,y); end
3315. 内摆线（星形线）x?acost,y?asint(x?y?a) hold on
t=0:0.1:10; for a=0:0.5:2; x=a.*(cos(t).^3); y=a.*(sin(t).^3); plot(x,y); end
232323
16. 圆的渐伸线（渐开线)x?a(cost?tsint),y?a(sint?tcost) hold on
t=0:0.1:10;
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