Dynamical Systems Are No Match for This High School Senior

In December we received a Maple application from a Mr. Forhad Ahmed, entitled "Analysis and Simulation of Simple Dynamical Systems". At first glance, it appeared to be a typical application by a physics professor to model multibody systems. What was not typical, we learned later, was Mr. Ahmed himself. It turns out Mr. Ahmed is now applying to Princeton and Cornell Universities ­ as a freshman.

Most physics students learn the mathematics and physics of multibody systems in the 2nd or 3rd year of university. But don't tell that to Mr. Ahmed, who taught himself classical mechanics and differential equations from textbooks as a senior at Columbus Alternative High School in Ohio. Simulation of three masses joined by springs, created by Forhad Ahmed's Maple application. The lower mass is free to swing, while the upper-right mass is free to slide horizontally.

Age of the author aside, Mr. Ahmed's Maple application is quite impressive in its own right. Not only does it solve the equations of motion of dynamical systems, it provides the user with object-oriented routines to build the physical system and generate the equations. For example, there are routines to add a new particle to the system with a given mass, position and velocity; add a spring with a given stiffness between two particles; and specify along which axes each particle is free to move (e.g., x-axis, y-axis, both or neither). After building the system, the user invokes another of Ahmed's routines to generate the system of equations from Newton's laws and solve them numerically with Maple's dsolve.

In one example, he demonstrates the motion of a metal tower subjected to vibrations at the base. He models the tower as eight masses bound into a lattice by stiff springs. The two masses at the base are subjected to horizontal vibrations with known amplitude and frequency.The user can view horizontalmotion plots of each individual mass or an animation of the tower as a whole.

Mr. Ahmed's Maple applications are available at http://www.mapleapps.com/categories/science/physics/html/Mechanical%20Systems.html and http://www.mapleapps.com/categories/science/physics/html/Satellite.html.

If Mr. Ahmed's Maple work is any indication, the physics community should look forward to a productive new member in a few years.

Article: Dynamical Systems Are No Match for This High School Senior