Please help i seem to be failing to understand what the following errors mean and how to correct for them.

%Script file for the Analysis of the double Pendulum(Chaos)
%Purpose : School Assignment
%written by : Yolanda Dube

g = 9.8;                       %gravitational Acceleration
l1 = 1;                         %length of the first rope
l2 = 1;                         %lenght of the second rope
m1 = 0.5;                    %mass of particle 1
m2 = 0.5;                    %mass of particle 2
t = 0:0.02:20*pi;         %time period
th1 = 45;                    %angular displacement
th2 = 0;                     %angular displacement
v1 = 0;                      %initial velocity of the first particle
v2 = 0;                      %initial velocity of the second particle
yi =  (pi/180).*[th1;0;th2;0];

%%using the differential equation tool
t0 = 0;
[t,y] = ode45(@yi,t0,t,f)

%%trajectory

x1 = l1*sin(y(1,:));
y1 = l1*cos(y(1,:));
x2 = l1*sin(y(1,:)) + 12*sin(y(3,:));
y2 = -l1*cos(y(1,:)) - 12*cos(y(3,:));
subplot(2,2,1)
xgrid

plot(x1,y1,'-ob')
plot(x2,y2,'-dr')
xtitle('TRAJECTORY')
subplot(2,2,2)
xgrid

plot(t, (180/pi)*y(1,:),'-ob')
plot(t,(180/pi)*y(3,:),'-dr')
xtitle('Angular displacement of m1 AND m2')
subplot(2,2,3)
xgrid

plot(t,(180/pi)*y(2,:),'-ob')
plot(t,(180/pi)*y(4,:),'-dr')
xtitle('Velocity of m1 AND m2')
subplot(2,2,4)
xgrid

plot(t,(180/pi).*y(1,:),(180/pi).*y(3,:),'k')

%%Looping our sytems of equations

function [ydash]=f(t,y)
    ydash(t,1)=y(2)
    ydash(t,2)=(1/((m1+m2)*l1-m2*l1*((cos(y(1)-y(3)))^2)))*(-m2*l1*(y(2)*y(2))*sin(y(1)-y(3))*cos(y(1)-y(3)) + m2*g*sin(y(3))*cos(y(1)-y(3)) - m1*l2*(y(4)*y(4))*sin(y(1)-y(3)) - (m1+m2)*g*sin(y1))
    ydash(t,3) = y(4)
    y(4) = (1/(l2-(m2*l2/(m1+m2))*((cos(y(1)-y(3)))^2)))*(l1*(y(2)*y(2))*sin(y(1)-y(3)) - g*sin(y(3)) + (m2*l2/(m1+m2))*(y(4)*y(4))*sin(y(1)-y(3))*cos(y(1)-y(3)) + g*sin(y(1))*cos(y(1)-y(3)))
end

[Matt J]

We don't know what errors you are getting. You haven't copy/pasted them for us.

[yolanda dube]

Sorry the errors that i am getting are as follows;

>> doubletrouble

Not enough input arguments.

Error in doubletrouble>f (line 53)

ydash(t,1)=y(2)

Error in doubletrouble (line 19)

[t,y] = ode45(@yi,t0,t,f)

[yolanda dube]

Apologies i am new to this service just figuring my way around:-)

[Stephen23]

yi is a 4x1 numeric, you cannot define a function handle from it by simply placing '@' in front of its variable name.

How to define valid function handles is covered quite well in the MATLAB documentation:

https://www.mathworks.com/help/matlab/function-handles.html

The fourth input argument to ODE45 is defined in the documentation as a structure of options for the ODE solver. Instead you called the function f without any input arguments (thus the error message you are getting). Even if you provided f with input arguments it does not return a structure of options, so it is not clear why you expect this to be a valid fourth input to ODE45.

I suspect that you should be providing a handle to f as the first input.

It is not clear what you expect defining the value of y at the very end of f is going to achieve.

Answer 1

[Stephen23]

I suspect that something like this is what you are trying to do (I fixed many small bugs):

g = 9.8;                     %gravitational Acceleration
l1 = 1;                      %length of the first rope
l2 = 1;                      %lenght of the second rope
m1 = 0.5;                    %mass of particle 1
m2 = 0.5;                    %mass of particle 2
th1 = 45;                    %angular displacement
th2 = 0;                     %angular displacement
v1 = 0;                      %initial velocity of the first particle
v2 = 0;                      %initial velocity of the second particle
y0 =  (pi/180).*[th1;0;th2;0];
ts = 0:0.02:20*pi;         %time period
fun = @(t,y)f(t,y,m1,m2,l1,l2,g); % parameterize function
[t,y] = ode45(fun,ts,y0)

t = 3142×1

0 0.0200 0.0400 0.0600 0.0800 0.1000 0.1200 0.1400 0.1600 0.1800

y = 3142×4

0.7854 0 0 0 0.7835 -0.1849 0.0013 0.1310 0.7780 -0.3704 0.0052 0.2636 0.7687 -0.5572 0.0119 0.3997 0.7557 -0.7460 0.0213 0.5409 0.7389 -0.9371 0.0335 0.6884 0.7182 -1.1312 0.0488 0.8438 0.6936 -1.3295 0.0673 1.0089 0.6650 -1.5318 0.0893 1.1839 0.6323 -1.7372 0.1148 1.3673

function ydash = f(t,y,m1,m2,l1,l2,g)
    ydash = nan(4,1); % preallocate!
    ydash(1) = y(2);
    ydash(2) = (1/((m1+m2)*l1-m2*l1*((cos(y(1)-y(3)))^2)))*(-m2*l1*(y(2)*y(2))*sin(y(1)-y(3))*cos(y(1)-y(3)) + m2*g*sin(y(3))*cos(y(1)-y(3)) - m1*l2*(y(4)*y(4))*sin(y(1)-y(3)) - (m1+m2)*g*sin(y(1)));
    ydash(3) = y(4);
    ydash(4) = (1/(l2-(m2*l2/(m1+m2))*((cos(y(1)-y(3)))^2)))*(l1*(y(2)*y(2))*sin(y(1)-y(3)) - g*sin(y(3)) + (m2*l2/(m1+m2))*(y(4)*y(4))*sin(y(1)-y(3))*cos(y(1)-y(3)) + g*sin(y(1))*cos(y(1)-y(3)));
end

See also:

https://www.mathworks.com/help/matlab/math/parameterizing-functions.html

[yolanda dube]

Thank you so much Stephen, Yeah atleast now i have someothing that is running. thanks so much for your help.

Answer 2

[Matt J]

Not sure what you are trying to do with ode45. The way you are invoking it does not match any syntax in the documentation. Perhaps this is what you meant,

[t,y] = ode45(@f,t,yi)

[yolanda dube]

Thank You so much Matt for your information it has made me understand more about the "ode45" module...

[Matt J]

You're welcome, but please Accept-click the answer that you feel resolved your question.