Ode45 I get wrong results.

Question

Arda Nova 2018-12-31

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/437764-ode45-i-get-wrong-results

评论： Arda Nova 2019-1-1

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

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madhan ravi 2018-12-31

why 13 any reason?

Arda Nova 2018-12-31

编辑：Arda Nova 2018-12-31

在 MATLAB Online 中打开

dydt(2)=-((9.81*sin(y(1)))/0.5);

At the bottom, acceleration is maximum. If you put 270 degrees acceleration comes 19.62 rad/sec^2 (Sorry I had made a mistake at taking the degree. Tried it too, wrong result). One think is for sure, acceleration should not be affected from me using radian or degrees. I don't even know where does the program gets the 3.something. If I knew then I would maybe solve the issue but, couldn't figure it out.

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Answer 1

Stephan 2019-1-1

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/437764-ode45-i-get-wrong-results#answer_354579

编辑：Stephan 2019-1-1

在 MATLAB Online 中打开

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