MATLAB: Ode45 I get wrong results.

ode45

function dydt = idn (t, y)
dydt = zeros(2,1);
dydt(1)=y(2);
dydt(2)=-((9.81*sin(y(1)))/0.5);
dydt = [0.78 0];
[t1,y1] = ode45(@idn, [0 20], dydt);
plot(t1,y1(:,2));
grid on;
This is a code for simple pendulum. When I use this code group, acceleration comes out wrong(it goes between max 3.. when it should be 13.). What am I doing wrong? When I use sind and put 45 degrees instead of sin and 0.78 radia, this time I get 30 ish something as a max result when it shouldn't change.
Original Eqn: Theta''=-g*sin(Theta)/ l

Best Answer

Hi,
ode45 integrates your second order ode two times. So the result of ode45 will be angle and velocity over time. To get acceleration you have to calculate it seperatly:
% initial conditions of angle and velocity
dydt = [pi/2; 0];
% integrat ode to get angle an velocity
[t1,y1] = ode45(@idn, [0 20], dydt);
% calculate acceleration
y1(:,3) = -9.81.*sin(y1(:,1))./0.5;
% plot results
plot(t1,y1(:,1),t1,y1(:,2),t1,y1(:,3));
grid on;
function dydt = idn(t, y)
dydt = zeros(2,1);
dydt(1)=y(2);
dydt(2)=-((9.81*sin(y(1)))/0.5);
end
Best regards
Stephan
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