Staircase Dynamics
by
J. J. P. Veerman
Portland State University, OR 97207.
Coauthors: G. Vasconcelos

We study the dynamics of certain systems that model a point particle  falling down a possibly tilted staircase under the influence  of gravity. The main task is to decide which orbits (as a function of the inclination of the staircase and the initial condition) eventually stop,  which ones do not stop but continue with bounded  velocity,  and which ones have unbounded velocity. For the simplest  of these models,  we can give a simple criterion that decides which  orbits acquire unbounded velocity,  and which don't (as a function of  initial conditions and inclination of the staircase). However,  for  the more realistic models the frontier between bounded and unbounded  behavior may well be a very complicated set. 

The study of these systems arose in an effort to better understand  the motion of invidual particles participating in 'granular flow',   such as sand flowing down a mound (avalanches). 

Date received: June 25, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagw-98.