Solving 2 second order differential equations

Question

Alastair Poore 2019-1-22

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/440984-solving-2-second-order-differential-equations

回答： Torsten 2019-1-23

Hi, I'm trying to solve two simultaneous differential equations in matlab following the code provided here https://uk.mathworks.com/matlabcentral/answers/425468-how-to-solve-simultaneous-second-order-differential-equations . This is the code I have managed to producde so far

syms  theta1(t) theta2(t) Dtheta1(t) Dtheta2(t)
g=9.81;
m1=1;
m2=1;
L1=1;
L2=1;
ode1= (-g*(2*m1+m2)*sin(theta1)-m2*g*sin(theta1-2*theta2)-2*sin(theta1-theta2)*m2*(Dtheta2^2*L2+Dtheta1^2*L1*cos(theta1-theta2)))/(L1*(2*m1+m2-m2*cos(2*theta1-2*theta2)));
[ode1, var1] = reduceDifferentialOrder(ode1,theta1);
ode2= (2*sin(theta1-theta2)*Dtheta1^2*L1*(m1+m2)+g*(m1+m2)*cos(theta1)+Dtheta2^2*L2*m2*cos(theta1-theta2))/(L2*(2*m1+m2-m2*cos(2*theta1-2*theta2)));
[ode2, var2] =reduceDifferentialOrder(ode2,theta2);
ode = [ode1; ode2;];
var = [var1; var2;];
[odes, vars] = odeToVectorField(ode);
ode_fun = matlabFunction(odes, 'Vars',{'t','Y'});
y0 = [0 0 0 0 0 0];
tspan = [0 15];
[t,y] = ode45(ode_fun,tspan,y0);
Dtheta1 = y(:,1);
theta1 = y(:,2);
Dtheta2 = y(:,3);
theta2 = y(:,4);