Maxima by Example: Ch. 7, 8, 9, 10, and 11

Dan Hatton wrote:
> On Sun, 3 May 2009, Robert Dodier wrote:
> 
>> Broad interest in nonlinear dynamics might have peaked around
>> 1995. One professor told me around that time, "I was doing nonlinear
>> dynamics before it was popular and I'll still be doing it when it is
>> unpopular again." If anyone knows what's happening in the nonlinear
>> world I'd be interested to hear about it.
> 
> By "nonlinear dynamics" do you mean "trying to solve theoretical
> physics problems that contain non-linear terms"?  If so, there's a lot
> of activity in fields I tend to read about, e.g.
> 
<cut>

That's along the lines of what I was thinking of. For work I'm doing, a 
CAS (maxima in this case) is the only way that I am able to even 
consider deriving my equations in enough detail to get the proper 
nonlinear terms. (Rather than doing the derivation by hand over and over 
again as I detect bugs).

I have also written some code that lets me automate the conversion of 
dimensionalized equations into nondimensional form, a super-handy tool.

I plan to use maxima to try to discover which terms have meaningful 
effects, and ultimately use FFT based techniques to solve the PDEs 
numerically to determine whether the overall effects are significant in 
a range of conditions that pertain to actual problems of interest in 
engineering.

In my case, the nonlinearities may be important at smallish space scales 
(a few mm) where finite element codes using linear models wouldn't cut 
it for example.

In the last few years I have seen several groups doing similar types of 
modeling in areas like materials mechanics, climate, and traffic 
modeling. Often they are coupling different length or time scales 
together to arrive at problems that are nonlinear at one scale coupled 
to a simplified linear problem at another scale.