solving a second order linear differential equation

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Eliraz Nahum on 23 Sep 2018
Answered: Eliraz Nahum on 23 Sep 2018
hello everybody, I was trying to solve a simple pendulum second order linear differential equation of the form y''=-(g/l)*sin(y) while using the ode45 function. since it's a second order equation I understood that I have to manipulate the problem, so it will fit the ode45.
The mathematical manipulation I did is described in the attached picture.
g=9.8;
l=0.5;
t_span=[0 30];
F=@(t,q) [q(2);-(g/l)*sin(q(2))];
[t,q]=ode45(@(t,q) F(t,q),t_span,teta0)

Mischa Kim on 23 Sep 2018
Edited: Mischa Kim on 23 Sep 2018
Almost there:
g = 9.8;
l = 0.5;
t_span = [0 30];
F = @(t,q) [q(2);-(g/l)*sin(q(1))]; % check your derivation
[t,q_t] = ode45(@(t,q) F(t,q),t_span,[teta0; tetad0])
This is a second order DE so you need two initial conditions, one for teta and one for tetad.

Eliraz Nahum on 23 Sep 2018
thank you very much... sometimes it's not about the code, but the mathematics :-)

R2018a