[Scilab-users] ODE : Second order coupled differential equations

[Cruz]

Hello everybody,

I have a system of 2 differential equations (Eq.1 and Eq.2) coupled of order
2 as shown in the attached image. Normally, I can easily find the solution
by transforming this system onto a system of order 1 by changing variables.

<http://mailinglists.scilab.org/file/t498030/ode.jpg> 

The variables theta and r are functions of time. I use the ODE solver
integrated in Scilab.

Here is my code :

------------------------------------------------------------------

t0 =  0; // initial time (s)
tmax = 30; // solving max time (s)
tinc = 0.005; // time increment (s)

t = t0:tinc:tmax;

// Differential equations system

function du = equadiff(t,u)

  // d for derivative with respect to time t
  // u(1) = theta
  // u(2) = d(theta)/dt
  // u(3) = r
  // u(4) = d(r)/dt
  // du(1) = d(theta)/dt
  // du(2) = d²(theta)dt²
  // du(3) = d(r)/dt
  // du(4) = d²(r)/dt²

  F1=1300;
  F2=1000;
  l=13;
  k=68000;
  menv = 112.14;
  m0 = 56.07;
  g=9.81;

  m = (menv - m0) * (1-abs(cos(u(1)))) + m0;

  du(1) = u(2);
  du(2) = (F2*sin(u(1)) + (F1-m*g).*cos(u(1)) - 2*m.*u(4).*u(2)) ./
(m.*u(3));
  du(3) = u(4);
  du(4) = ((F1-m*g).*sin(u(1)) - F2*cos(u(1)) - k*(u(3)-l) +
m.*u(3).*u(2).*u(2)) ./ m;

endfunction

// Integration

u0 = [0,0,13,0];
[u] = ode(u0,t0,t,equadiff);

------------------------------------------------------------------

The problem is that the output of the solver, [u], should be a matrix of 4
lines and 6001 columns:

4 lines:

u (1) = theta
u (2) = d (theta) / dt
u (3) = r
u (4) = d (r) / dt

6001 columns:

tmax / tinc = 6000 time step + the initial instant t0 = 6001

At the end of the calculation I get

size (u)

ans =

1. 24004.

instead of

4. 6001.

It seems to me to proceed in the standard way for this type of problem.
Someone have any idea why it doesn't work?

Thanks in advance to all !










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