2nd order nonlinear ode

Hii guys, i need help my term project, please help me to solve this equation

6.6842e-11y'' + 3.4609e-06y' + 17.9194y = 4.3618e-18 / (1.1800e-06-y)^2

is it possible to use ode45, how to represent the function in state space?

Thank You so much best regards

Answer 1

[Star Strider]

While I appreciate your confidence in me, I would not deprive you of the fun of evaluating this yourself. I will guide you through the analysis and setting up your ODE in terms ode45 will understand.

Your ODE is of the form:

c(1)*y" - c(2)*y' + c(3)*y = f(y)

that is actually straightforward to analyse. Since y"=(y')', your ODE can be expressed in three terms here, y(1) = y', y(2) = y(1)' = y", and y.

So we have:

y(1) = y(2)
y(2) = (f(y(1)) - c(3)*y(1) - c(2)*y(2))/c(1)

I have every confidence that you can take it from here. The documentation for ode45 will also help you.

If you have problems getting your code to work, post your ODE function and your ode45 call and related code, and I will help you troubleshoot it.

[Iswan Pradiptya]

please explain about this, because I found inconsistency here You define y' = y(1), so y''=y(1)'=y(2) (ok, i got this idea), but why after that you defined y(1) = y(2) ??? Thanks for your helps

[Torsten]

dy(1) = y(2)
dy(2) = (f(y(1)) - c(3)*y(1) - c(2)*y(2))/c(1)

Best wishes

Torsten.

[Star Strider]

@Torsten — Thank you.

[Iswan Pradiptya]

     function d2xdt2 = solveit(t,x)
     d2xdt2 = zeros(2,1);
     global m_eff c k e_d A V_pi d
     d2xdt2(1) = x(2);
     d2xdt2(2) = (e_d*A*V_pi^2)/(2*d*d - 2*d*x(1) + x(1)*x(1)-k/m_eff *x(1)- c/m_eff*x(2) ;

t0 = 0; tf = 2e-3; tstep = 500;

interval = linspace(t0,tf,tstep);

x0 = 0; v0 = 0;

initial = [x0 v0];

[t, x] = ode45(@solveit,interval,initial); plot(t,x(:,1)); title('x'); figure plot(t,x(:,2)); title('x dot');

then for code

[Iswan Pradiptya]

the result is not convergence ,..

[Star Strider]

Correct. The system is unstable. I suspect you are supposed to design a controller for it.