Symbolic manipulation and integration / not enough input argument

Question

Mauro De Francesco 2018-10-9

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https://ww2.mathworks.cn/matlabcentral/answers/423003-symbolic-manipulation-and-integration-not-enough-input-argument

评论： Stephan 2018-10-10

Hello, I have two symbolic functions that i want to integrate. I have converted with matlabFunction the equations into a file here reported:

function DY = Pendulum(theta,w,l)
%PENDULUM
%    DY = PENDULUM(THETA,W,L)
%    This function was generated by the Symbolic Math Toolbox version 8.2.
%    09-Oct-2018 12:30:20
DY = [w;(sin(theta).*(-9.81e2./1.0e2))./l];

Where the variables are theta and w and l is a constant. Now I want to integrate like this:

X0 = [90*pi/180 ; 1.2];
[tout,yout] = ode45(@Pendulum, [0 5], X0, 2 );

and i get the error Not enough input arguments.

Can someone please explain what is the problem?

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Answer 1

madhan ravi 2018-10-9

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https://ww2.mathworks.cn/matlabcentral/answers/423003-symbolic-manipulation-and-integration-not-enough-input-argument#answer_340488

编辑：madhan ravi 2018-10-9

在 MATLAB Online 中打开

X0 = [90*pi/180 ; 1.2];
[tout,yout] = ode45(@Pendulum, [0 5], X0)
plot(tout,yout(:,1),'r' )
hold on
plot(tout,yout(:,2),'b')
function DY = Pendulum(theta,w,l)
%PENDULUM
w=1;   % error was here because w and l were not defined , I gave w and l as an example change it according to your values
l=2;
%    DY = PENDULUM(THETA,W,L)
%    This function was generated by the Symbolic Math Toolbox version 8.2.
%    09-Oct-2018 12:30:20
DY = [w;(sin(theta).*(-9.81e2./1.0e2))./l];
end

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Stephan 2018-10-10

编辑：Stephan 2018-10-10

@Madhan: The ode of pendulum is a second order ode. The system of odes given here is the converted first order sytem which is equivalent to the equation of pendulum i think.

madhan ravi 2018-10-10

@stephen maybe but I’m stuck at this point .

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Answer 2

Walter Roberson 2018-10-9

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https://ww2.mathworks.cn/matlabcentral/answers/423003-symbolic-manipulation-and-integration-not-enough-input-argument#answer_340494

在 MATLAB Online 中打开

ode45(@(theta, w) Pendulum(theta, w, SomeValueForL)

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Walter Roberson 2018-10-9

You are copying all of w into the output and another value as well. w is length 2 so the result is length 3. You should probably be using w(2) instead of w in constructing the output

Walter Roberson 2018-10-9

在 MATLAB Online 中打开

w = sym('w', [2 1]);
syms theta L
om_d = .... something involving w, theta, and L
Y = [w(1) ; om_d];
matlabFunction(Y, 'File', 'Pendulum', 'Vars', {theta  w L},...
  'Outputs',{'DY'});
X0 = [90*pi/180 ; 1.2];
L = 2;
[tout,yout] = ode45(@(theta, w) Pendulum(theta, w, L) , [0 5], X0);

... When I am typing on my phone in the middle of the night, I sometimes only give the outline of the change, as editing by poking with one figure is not all that productive.

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Answer 3

Stephan 2018-10-9

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https://ww2.mathworks.cn/matlabcentral/answers/423003-symbolic-manipulation-and-integration-not-enough-input-argument#answer_340495

编辑：Stephan 2018-10-10

在 MATLAB Online 中打开

Edit

Here is another approach, inspired by Walters answer:

syms phi(t) g l
eqn = diff(phi,t,2) + g/l * sin(phi) == 0;
eqn = odeToVectorField(eqn);
Pendulum = matlabFunction(eqn, 'File', 'Pendulum','vars',{'t','Y','g','l'},'Outputs',{'DY'});
X0 = [90*pi/180, 1.2];
l = 2;
g = 9.81;
[tout,yout] = ode45(@(t,Y)Pendulum(t,Y,g,l), [0 5], X0);
plot(tout,yout(:,1),'r',tout,yout(:,2),'b')

With the resulting Pendulum.m file:

function DY = Pendulum(t,Y,g,l)
%PENDULUM
%    DY = PENDULUM(T,Y,G,L)
%    This function was generated by the Symbolic Math Toolbox version 8.2.
%    10-Oct-2018 08:21:21
DY = [Y(2);-(g.*sin(Y(1)))./l];

Theta and w are Y(1) and Y(2) here.

Best regards

Stephan