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Nonlinear dynamics of a ball rolling on a surface

Publication ,  Journal Article
Virgin, LN; Lyman, TC; Davis, RB
Published in: American Journal of Physics
March 1, 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.

Duke Scholars

Published In

American Journal of Physics

DOI

ISSN

0002-9505

Publication Date

March 1, 2010

Volume

78

Issue

3

Start / End Page

250 / 257

Related Subject Headings

  • General Physics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

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ICMJE
MLA
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Virgin, L. N., Lyman, T. C., & Davis, R. B. (2010). Nonlinear dynamics of a ball rolling on a surface. American Journal of Physics, 78(3), 250–257. https://doi.org/10.1119/1.3263169
Virgin, L. N., T. C. Lyman, and R. B. Davis. “Nonlinear dynamics of a ball rolling on a surface.” American Journal of Physics 78, no. 3 (March 1, 2010): 250–57. https://doi.org/10.1119/1.3263169.
Virgin LN, Lyman TC, Davis RB. Nonlinear dynamics of a ball rolling on a surface. American Journal of Physics. 2010 Mar 1;78(3):250–7.
Virgin, L. N., et al. “Nonlinear dynamics of a ball rolling on a surface.” American Journal of Physics, vol. 78, no. 3, Mar. 2010, pp. 250–57. Scopus, doi:10.1119/1.3263169.
Virgin LN, Lyman TC, Davis RB. Nonlinear dynamics of a ball rolling on a surface. American Journal of Physics. 2010 Mar 1;78(3):250–257.

Published In

American Journal of Physics

DOI

ISSN

0002-9505

Publication Date

March 1, 2010

Volume

78

Issue

3

Start / End Page

250 / 257

Related Subject Headings

  • General Physics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 02 Physical Sciences
  • 01 Mathematical Sciences