[sdiy] semi OT: nonlinear idiot needs help

[Ian Fritz]

Martin --

There is no general theory of non-linear systems, as different systems
generally require entirely different treatments. The world of non-linear
systems is huge compared to the puny little world of linear ones.

There are many books on non-linear systems. A good intro is "Chaotic
Dynamics" by Baker and Gollub. If you are interested in musical
applications, you could start at my website, where I have given an
elementary discussion of the dynamics of a clarinet model. Here is a more
advanced musical instrument reference: "Mechanics of Musical Instruments",
by A. Hirschberg, J. Kergomard and G. Weinreich.

You are starting on a fascinating voyage of exploration!

  Ian

----- Original Message -----
From: "Czech Martin" <Martin.Czech at Micronas.com>
To: "Sdiy (E-Mail)" <synth-diy at dropmix.xs4all.nl>
Sent: Wednesday, September 05, 2001 6:31 AM
Subject: [sdiy] semi OT: nonlinear idiot needs help


> I think by now I have a good position in understanding linear
> time invariant systems. I mean convolution, transforms,
> transfer function etc. (thanx Magnus, Don, Juergen and all
> the others who teached me).
> This linear stuff seems pretty much complete and all worked out.
>
> But: we all know (not only guitar players) that the
> real fun starts with nonlinearity at least.
>
> I only know little about nonlinear or time varying systems.
> I knew basic control theory about that, and some chaos
> stuff like Lorentz attractors and and Runge-Kutta
> integration of first order non linear differential
> equations and stuff like that.
>
> Is there anything like a complete theory of said systems?
> I guess it's far away from completeness and still growing.
> Any hints?
>
> Thanx.
>
> m.c.