Nonlinear dynamics of a ball rolling on a surface

TitleNonlinear dynamics of a ball rolling on a surface
Publication TypeJournal Article
Year of Publication2010
AuthorsLN Virgin, TC Lyman, and RB Davis
JournalAmerican Journal of Physics
Start Page250
Pagination250 - 257
Date Published03/2010

An underlying potential energy function can provide visual and intuitive insight into a system's stability and overall behavior. In particular, the motion of a ball moving along a curve or surface in a gravitational field provides a macroscale demonstration of interesting dynamics. We investigate the motion of a small ball rolling along a smooth two-dimensional potential surface. A direct experimental realization of this situation is suitable for demonstrating some classic features of nonlinear dynamics. The results of numerical simulations are directly compared with experimental data. To better characterize the dynamical behavior of the ball, especially when it is undergoing chaotic motion, several descriptive measures are discussed, including time-lag embedding, initial condition maps, power spectra, Lyapunov exponents, and fractal dimensions. © 2010 American Association of Physics Teachers.

Short TitleAmerican Journal of Physics