On 09/04/2011 09:01 AM, Steve Sullivan wrote:
> Hi,
>
> I'm a newbie to maxima and am trying to solve
> or at least simplify a pair of 3D equations.
>
> If v is a vector valued function of x, y, z:
> div(v) = 0 # del . v = 0
> curl( cross( curl(v), v)) = 0 # del X ((del X v) X v) = 0
>
> My attempts have been fruitless ... do you have any suggestions?
>
> load("vector3d.mac");
>
> v : [vx,vy,vz];
> depends([vx,vy,vz], [x,y,z]);
>
> solve( [div(v) = 0, curl( cross( curl(v), v)) = 0], v);
Since v is a vector field, and the equations you've given are (partial)
differential equations there need to be at least some boundary
conditions described.
unless I'm being silly and there is only a single vector field that can
satisfy these equations (perhaps the constant field or something like
that) this is simply not the kind of thing you can hand to maxima's
solve and expect an answer from. Solve is basically for solving
algebraic equations.
what did you expect or want Maxima to do here? Perhaps we can point you
to something more helpful.