Solving coupled 2nd order differential equations

Hello,

I am trying to solve the following 2nd order coupled diffrential equations:

So i started with the following code - I don't know if it's right at first place and i don't know how to continue (using ode45).

I want to plot three things : plot(x,y) , plot(t,y) , plot(t,x).

Any help will be appreciated .

syms O a g L x(t) y(t) t Y ;
dx = diff(x);
d2x = diff(x,2);
dy = diff(y);
d2y = diff(y,2);
Eq1 = d2x == 2*O*sin(a)*dy - (g/L)*x(t);
Eq2 = d2y == -2*O*sin(a)*dx - (g/L)*y(t);
[VF,Subs] = odeToVectorField(Eq1, Eq2)
ftotal = matlabFunction(VF,'Vars',{O,a,g,L,Y});
O=rand;
a=rand;
g=9.81;
L=rand;

Answer 1

[Star Strider]

Try this:

syms O a g L x(t) y(t) t Y ;
dx = diff(x);
d2x = diff(x,2);
dy = diff(y);
d2y = diff(y,2);
Eq1 = d2x == 2*O*sin(a)*dy - (g/L)*x(t);
Eq2 = d2y == -2*O*sin(a)*dx - (g/L)*y(t);
[VF,Subs] = odeToVectorField(Eq1, Eq2)
ftotal = matlabFunction(VF,'Vars',{t,Y,O,a,g,L});
O=rand;
a=rand;
g=9.81;
L=rand;

tspan = [0 25];                                             % Choose Appropriate Simulation Time
ic = [0 1 0 1];                                             % Choose Appropriate Initial Conditions
[t,y] = ode45(@(t,y) ftotal(t,y,O,a,g,L), tspan, ic);

figure
plot(t, y)
grid
legend(string(Subs))

The initial conditions and parameters need to be appropriate for the simulation you want to do. The simulation time can be anything appropriate.

[Joe Hasrouny]

Thank you very much it worked.

[Star Strider]

As always, my pleasure!

I added the ‘t’ argument since it is necessary to include the independent variable, and slightly rearranged the others.

[Haseeb Hashim]

Hi I wanted to ask 1 thing the solution vector y contains solution in what order i-e the x displacement first or y displacement first along with the velocities please respond quick if you can

[Star Strider]

@Haseeb Hashim — The first column of the integrated result coresponds to the first differential equation in the original system, the second column to the second differential equation, and so for any others.