Evaluating an ODE until you reached a certain distance using a while loop: Train/distance problem

Hello, I was wondering how you'd evaluate a ode until it reaches a wanted distance. For me I'm trying to code it so that it run until R is equal to the distance, which is 3. Any tips on were I'm going wrong? Thanks

    % code
 function tr()
 gr = 4.66; r = 1; D = 2;
 options = odeset('events', @location);
 [t,R] = ode45(@coupled,[0,3],[r;3],3);
 V=R(1,2);
 plot(t,R(:,1),'o',t,R(:,2),'o');
 shg
 %end
 [T1,Y1,te,ye,ie]=ode45(@coupled,[1:1:50],  [1;3],options);
 disp(te);

 function [lookfor,stop,direction]=location(t,y)
 lookfor=y(2)-3; % Stop at 3 
 stop=1;
 direction=0;
 end
 function dYdt = coupled(w,Y)
    dYdt = zeros(1,2);
    dYdt = [Y(1);-(pi^2/6)^2*cos(pi*w)^2-gr*sin((pi/8)*cos(pi*w))];
end
end

end

[Are Mjaavatten]

It is not clear to me what you are trying to do. Do you want to:

1) Solve the ODE on the interval [0,3] and vary the initial value of t until R(x=3) = 3?

2) Solve for an interval [0,xmax] so that R(x=xmax) = 3?

Or something else entirely?

In case 2) have a look at the option 'events' in odeset .

[panacean]

I apologize for not being clear. so I have a train on a set of tracks and I'm trying to calculate how long it will take for my train to get to a distance of 3 miles. where r is the current distance of the train and D is the goal of 3 miles.

[Are Mjaavatten]

I am still confused. Is x and R both distances? Could you post your coupled function and explain the meaning of the variables x, t and R?

[panacean]

So added more of my code, with some changes, I'm trying to find how long it takes the train to go 3 miles. My ode with the options event isn't doing the search like I wanted it to do. Any tips?

[Are Mjaavatten]

I would still like a better explanation of what you are trying to do. If I interpret your function coupled(w,Y) correctly, you try to so solve the coupled differential equations

What is the independent variable w? Time? What are the two components of Y. (Is Y(1) = R?).

Note that your equations are not coupled at all, but two independent differential equations. Note also that the variable gr must be given a value.

The analytical solution is:

I am not sure that this is what you want. Please give a better description of the original problem.

Answer 1

[Jan]

lookfor=y(1)+3

This stops at y(1) == -3, not +3. You want:

lookfor = y(1) - 3;

[panacean]

Okay I changed it, still not working. Is this the right way to go about it? Trying to see how long it takes for r which starts at 1 takes for it to get to 3 miles. Changed my code above. Any tips would be great.

[Torsten]

dYdt = (pi^2/18)^2*r*sin(pi*t).^2-gr*sin(pi/16.*cos(pi*t);

- "r" and "gr" are undefined 
- a closing parenthesis is missing after "sin(pi/16"
- the solution variable "y" is not used in the calculation of dYdt.

[panacean]

Sorry I posted some older code.

[Torsten]

If you set

   lookfor = y(2)-3;

you search for the time t where velocity (y') becomes 3. I think you mean

   lookfor = y(1)-3;

Best wishes

Torsten.

[Jan]

@panacean: How can we help you to find the error in the code, if all we see is an older version? "Still not working" does not allow to understand, what you observe. Without the code and information about what the code does, I cannot understand, what the problem is.

Answer 2

[Torsten]

Use the "Event" option of ode45 to locate the t-value at which R=3.

Best wishes

Torsten.

[panacean]

Added my code with the changes, still coming out right. Any tips? The Event option is definitely the right way to go though.