On Tuesday, June 26, 2012 7:11:50 AM UTC-4, Eric Kangas wrote:
>
> Hi,
>
> First of all I am using a coupled 2sd ODE.
>
> First step was to declare variables:
>
> a,l,x,y,u,v,xdot,ydot,udot,vdot = var('a,l,x,y,u,v,xdot,ydot,udot,vdot',
> domain = RR)
>
>
> Second step turn the two 2sd ODE into four 1st ODE.
>
> xdot = u;
>
> ydot = v;
>
> udot = -(1-a)*((x-a)/(sqrt((x-a)^2 + y^2))^3)-a*((x+1-a)/(sqrt((x+1-a)^2 +
> y^2))^3)+x+2*v;
>
> vdot = -(1-a)*(y/(sqrt((x-a)^2 + y^2))^3)-a*(y/(sqrt((x+1-a)^2 +
> y^2))^3)+y-2*u;
>
>
>
At this point you should be able to do
V(x,y,u,v) = [xdot,ydot,udot,vdot]
V.diff()
to get the Jacobian matrix. It's true that we don't implement eigenvalues
for such generic symbolic matrices - presumably in general the computation
could take arbitrarily long or be too difficult for any system?
Also, I don't know why the determinant didn't work for you.
expand((V.diff()-diagonal_matrix([l,l,l,l])).det()).coeffs(l)
gets you go dN2, though for whatever reason I get only three things there
instead of your four.
Can you do this same process with a less complex system to show what *does*
work? The coefficients here are ridiculously huge and so I'm not sure
what's happening. At any rate trying this with some random expressions
(didn't do the solving) doesn't give this hang.
>
>
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