ODE45 for a System of Second-Order Equations

I need to solve these equations and plot the solutions for theta(t) and phi(t) when 0<t<4. I'm not super familiar with ode45, can anybody help? Thank you

Answer 1

[Star Strider]

I didn’t see this earlier.

I’m sure you will find the odeToVectorField and matlabFunction functions helpful.

[Caleb Rudick]

I know how to apply those functions to individual second-order ODEs, but how would I apply that to this system?

[Star Strider]

First, you need to express the derivatives in terms of ‘theta’, ‘diff(‘theta)’, and ‘diff(theta,2)’, and the others similarly. Then:

[VF,Subs] = odeToVectorField(eqn1,eqn2,eqn3)

with ‘VF’ as an argument to matlabFunction, along with chosen arguments using the 'Vars', name-value pair.

Also, add ‘t’ and ‘Y’ to the syms declaration. See the documentation for details.

[Caleb Rudick]

Thanks, still having issues. Am I missing something?

[Star Strider]

My pleasure!

I cannot read that image, and obviously I cannot run the code to check it.

However the problem is likely that ‘eqnSystem’ needs to be presented to ode45 as:

[t,y] = ode45(@t,y)eqnSystem(t,y,theta,phi,omega_C), [0 4], initVals);

then:

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

to see the results.