Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

periodic accelerated potential



I've found a way of solving an interesting but messy problem in
MAPLE. Some folks may be interested in trying it by adapting the
resources on my web page like I did, or they may find a 'better' way
to do it.

In the July 1997 Physics Today, starting on page 30 there is a
discussion of atoms in an accerating periodic potential. The authors
state that the classical solution for this problem depends on initial
conditions, and that the potential is effectively 'tilted' due to the
acceleration.


This is a 1-D potential in the x-direction, with gravity in the
y-directon. The 'tilt' of the potential is going to occur through the
principle of equivalence, since the accelerating frame may be
replaced with an inertial frame which has an additional
'gravitational force' in the x-direction.

The math for this situation quickly gets messy, so I tried adapting a
MAPLE solution from the Physics Resource Packets (see my home page,
below). This solution can be found under Theoretical Mechanics
Maple/Mathematica Resources in a program called 'Table'.

'Table' is the famous problem of mass m on a smooth tabletop
connected to hanging mass M via a cord passing through a hole in the
tabletop. 'Table' goes through Lagrange's equations and obtains a
numerical solution, which is then graphed.

The adaptation of 'Table' mainly consists of deleting the angular
variable, and renaming things for the radial variable. As always, I
made a bunch of errors and initially thought the graphs were wrong,
but now I'm fairly sure the graphs are making sense.

This is a pretty good application for a powerful engine on a complex
problem. I'd be interested to learn if others like this approach or
find some simpler (Interactive Physics?) way to model it.

--

Mike

===============================================================
Mike Moloney
moloney@nextwork.rose-hulman.edu
Dept of Physics & Applied Optics (812) 877 8302
Rose-Hulman Institute of Technology Terre Haute, IN 47803
http://www.rose-hulman.edu/~moloney