Question

matlab物体下落运动建模一个质量为75kg的物体在某一高度静止下落,空气阻力F与v的关系满足F=-kv^2,其中常数

Answer 1

法一：

v=dsolve('Dv=g-k*v^2/m','v(0)=0');

x=dsolve('D2x=9.81-0.22*Dx^2/75','x(0)=0','Dx(0)=0');

m=75;

g=9.81;

k=0.22;

t=0:0.1:25;

v=subs(v);

x=subs(x);

subplot(211)

plot(t,v)

subplot(212)

plot(t,x)

法二：

function bb

options = odeset('RelTol',1e-4,'AbsTol',[1e-4 1e-4]);

[t,y] = ode45(@fun,[0,25],[0,0],options);

subplot(211)

plot(t,y(:,1))

subplot(212)

plot(t,y(:,2))

end

function dy=fun(t,y)

m=75;

g=9.81;

k=0.22;

dy=zeros(2,1);

dy(1)=g-k*y(1).^2/m;

dy(2)=y(1);

end