Spring 1995

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Announcements

 

The Forced Damped Pendulum: Chaos, Complication and Control
By John H. Hubbard

In this paper, the author shows that a “simple’’ differential equation modeling a garden-variety damped forced pendulum can exhibit extraordinarily complicated and unstable behavior. While instability and control might at first glance appear contradictory, we can use the pendulum’s instability to control it. Such results are vital in robotics: the forced pendulum is one of the basic subsystems of any robot.

The Great Escape
By Alejandro Montes

This project is a model involving a nonlinear-first order differential equation that can be separated to give the path of a boat under the influence of wind.

Model Neurons and Fast-Slow Systems
By Thomas LoFaro; K.D. Cooper; Ray Huffaker

This is the first in a series of three articles on exercises that bring together recent developments in the environmental and life sciences with a modern dynamical systems approach to mathematical modeling. Each exercise combines varying degrees of mathematical modeling techniques, computer assisted phase plane analysis, and mathematical analysis. These exercises are designed for use in upper division courses both in mathematics and other disciplines using these techniques, but, with some adaptation, they could be used in an introductory course if sufficient background is provided.

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