How can I graph a "system" of ODEs?

I am trying to model a shape that is defined with multiple differential equations. For reference, the variables are x and y (from the normal Cartesian plane) and then S (arc length) and theta (angle of the arc length with the horizontal).

The equations are:

dtheta/dS = -sin(theta)/x + y - 2H (a constant)

dx/dS = cos(theta)

dy/dS = sin(theta)

I'm just wondering if MatLab has an easy way to do this. If not, how could I set up a modified Euler's Method to solve this?

[Star Strider]

If you haven’t already, see:

http://www.mathworks.com/help/techdoc/ref/ode23.html

to start with.

[Michael]

Seen it. Didn't really help me. I've used ode45 on a 2nd order ODE, but have never used these with systems.

Answer 1

[Star Strider]

Is this what you want to do?

          % dThXYdS(1) = theta(S), dThXYdS(2) = x(S),  dThXYdS(3) = y(S) 
          H = 10;
          dThXYdS = @(t,XYTh) [-sin(XThXY(1))/ThXY(2) + ThXY(3) - 2*H;  cos(ThXY(1));  sin(XYTh(1))];

          x0 = [0.1; 0.1; 0];

          Tspan = [0:0.01:2]';

          [T ThXY] = ode45(dThXYdS, Tspan, x0);

          figure(8)
          plot3(ThXY(:,1), ThXY(:,2), ThXY(:,3))
          xlabel('X(S)')
          ylabel('Y(S)')
          zlabel('\Theta(S)')
          grid

I have no idea what you intend for H or the rest, but this seems to work. I named the variable ThXY to denote the vector as [Theta(S); X(S); Y(S)].

NOTE: This is a duplicate of 'System of arc-length defined ODEs with ode45'.