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Matlab: Solving two second order differential equations

  1. Dec 17, 2008 #1
    1. The problem statement, all variables and given/known data
    Write a function and solver for the chaotic motion of stars in a galaxy

    Initial conditions:

    x at time zero = 0
    velocity of x at time zero = 0.3
    y at time zero = 0
    velocity of y at time zero = 0

    Time period 2 to 200 with an interval od 0.02

    2. Relevant equations

    This gives rise to the equations:

    d^2x/dt^2= -x-2xy;

    d^2y/dt^2= -y-x^2+y^2.

    And this gives rise to the four first-order equations

    dx/dt=velocity of x

    dvelocity of y/dt = -x -2xy

    dy/dt = velocity of y

    dvelocity of y/dt = -y=x^2+y^2

    3. The attempt at a solution

    This is my first time learning matlab and all the examples we were shown until now dealt with first-ODEs. I've made lots and lots of attempts at the solution, all coming up with all kinds of errors like undefined variables on Matlab. Basically my problem is that I can't figure out how to structure the function and solver for so many different terms.

    One hopeless attempt was:

    velocity of x to be Vx
    x to be x
    velocity of y to be Vy
    y to be y

    Is it supposed to look like:

    function q=func(t,x,y)
    q=[Vx; -x-2*x*y; Vy; -x^2+y^2]

    And the solver is


    I'm so confused on so many points. I don't think [x,y]=ode45(...) is right, but I don't know if it should be [t,x], [t.y] or whatever. Likewise, I know I'm meant to plot (x,y) for different time intervals, so do write plot(t,x,y)? I don't even know what [] is supposed to be for, only that it's in the notes and all the other examples I can find.

    I tried so many different variations, tried to look it up in books and on the web for 7 hours straight yesterday and 2 more today and I'm feeling quite miserable about matlab. Our notes aren't helpful at all, using different variations of names for x and y for different problems which was so confusing. I'd be so appreciative for any general help on how to structure function and solver, or even direct me to a book or website that deals with two second-ODEs.

    Is it just meant to look like:

    function name = another function name(time, variable 1, variable 2)
    name=[RHS equation 1;RHS equation 2;RHS equation 3;RHS equation 4];

    And the solver:

    initial conditions 1 = [x];
    initial conditions 2 = [y];
    initial conditions 3 = [z];
    constant = [a];
    t = [...;...;...]
    [?]=ode45(@function name,t, initial conditions 1, initial conditions2, initial conditions 3, [], constant);
    plot (?)

    Many thanks
    Last edited: Dec 17, 2008
  2. jcsd
  3. Dec 18, 2008 #2
    Never mind, figured out where I went wrong.

    Learning physics by trial and error...hmrph.
  4. Dec 19, 2008 #3
    thats pretty much how you learn matlab =\
  5. Dec 19, 2008 #4
    Feels like how I've learned the whole of my classical mechanics module - it's not very efficient!
  6. May 17, 2011 #5
    I'm also trying to solve two second ODE's for a different physical quantity. Could you please let me know the right ode structure.
    Thanks a lot in advance.

    Many thanks,
  7. May 18, 2011 #6
    Got it...
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