[Newbie:] How to discard higher orders of variables?

On Wed, Jul 11, 2007 at 09:46:12PM +0200, Schirmacher, Rolf wrote:
> Hello Daniel,
> 

> So, what would the "real world" look like? I have attached a wxMaxima input
> file as a starting point. Everything looks quite simple so far. The next
> step would be to loosen the n:0 restriction and generate cut-on frequency
> formulas for arbitrary n. These formulas are given in the literature, but at
> the moment, reproducing them includes some manual substitutions for me. You
> might try, it is not that bad...


Another thing I tried:

taylor(det,beta,0,2);

This has a factor of kappa^2 multiplying it, so eliminate that:

expr:ratsimp(%/kappa^2,beta);

take each of the coefficients of this taylor series (beta^0 and
beta^2) and extract them with ratcoeff. 

coef0: ratcoeff(expr,beta,0);
coef2:ratcoeff(expr,beta,2);

eliminate terms in these coefficients that have kappa^3 or higher, and
Omega^3 or higher using ratsubst, or ratweight if you prefer.

Reconstruct the taylor series using the truncated coefficients.

solve for kappa.

I get:

 ratsimp(%);
                                                2       2
(%o166) [kappa = - Omega sqrt(- ((4 nu - 6) beta  + 2 nu  + nu - 3)
                  2                2        3       2                 2     3
/(((7 nu - 3) beta  + nu - 1) Omega  + (3 nu  - 3 nu  - 4 nu + 4) beta  + nu
     2                                                  2       2
 - nu  - nu + 1)), kappa = Omega sqrt(- ((4 nu - 6) beta  + 2 nu  + nu - 3)
                  2                2        3       2                 2     3
/(((7 nu - 3) beta  + nu - 1) Omega  + (3 nu  - 3 nu  - 4 nu + 4) beta  + nu
     2
 - nu  - nu + 1))]


Again, a lot of assumptions, but perhaps they work out well enough for
your purposes? At least the maxima related techniques should be
helpful to you, even if the math doesn't work out.

-- 
Daniel Lakeland
dlakelan at street-artists.org
http://www.street-artists.org/~dlakelan