Re: Forced damped pendulum

[Charles Crummer <ccrummer@cats.ucsc.edu>]

> > Aha! Now we have it.
> > The motion of the pendulum is chaotic.
>
> That second degree of freedom did it. The best thing about
> chaotic motion is that it is not amenable to analysis in
> closed form, at least if we are talking about physics. The
> student should not be left with the idea that he is doing
> physical modeling in his investigation of ideal nonlinear
> differential equations.
>
> The spreadsheet approach I suggested earlier now seems
> even more appropriate.
>
> Leigh

At UCSC, we have a 2-DoF pendulum with different lengths in x and y.  It is
not chaotic, of course, but I want to add a Wilberforce pendulum as the
bob.  This will give 4-DoF.  With set screws, it will be possible to stop
off the last 2 degrees.  Adding them one at a time should produce chaos.
The interesting thing is that the nonlinearity will only come from the
coupling.  Each DoF is linear on its own.  An interesting project is to
simulate the motion with an analog computer.  It's on my list too.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
There is no time -- only clocks.  -- N. D. Mermin

Quantum Mechanics: The dreams stuff is made of

Relativity is the study of things that aren't.  There *is* something out there.

The main prerequisite to learning is not knowing.

OK, so what's the speed of dark?

Black holes are where God divided by zero.


Charles Crummer, PhD
Lower Division Physics lab mgr.
Physics Dept, Kerr Hall
University of California
Santa Cruz, CA  95064
(408)459-4154o
(408)459-3043FAX
(408)662-3635h
Office: Thimann Labs 111D