In preparation for an exciting Short Term, Nate looked into showing the path of a particle as it moves along a constrained path. First he considered the case of a bead down a wire, then a rolling ball down a track. Later he considered the behavior of a loosely bound particle (e.g. a zip line). When considering the forces on a curved track, it is important to understand just how curved the track is. Mathematically, we can look at tangent circles, also known as osculating circles.

Each of the following links leads to a page with additional examples. The animation on this page is an example of what you will find on the linked page. Each animation runs a different amount of time; to see the page's animations again, click "Refresh" on your web browser.


Bead on a wire
 
Osculating circles
 
Rolling ball
 
Loosely bound particle
 

To look at the webpage Nate set up, go to http://abacus.bates.edu/~nstambau/.




Roller Coasters Home Page | History of the Class | Class Calendar | Animations | Photos and Videos | Syllabus | Bates Mathematics Department

All content above relates to Math s45K, Roller Coasters: Theory, Design, and Properties, offered during Short Term 2005 at Bates College in Lewiston, Maine.
 
Please send comments or questions to Meredith Greer at mgreer@bates.edu.
 
Page last updated 6/28/2005.