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TECHNICAL PAPERS

The Motion of a Rolling Polygon

[+] Author and Article Information
E. M. Beunder, P. C. Rem

Delft University of Technology, Mijnbouwstraat 120, 2628 RX Delft, The Netherlands

J. Appl. Mech 70(2), 275-280 (Mar 27, 2003) (6 pages) doi:10.1115/1.1481893 History: Received December 12, 1999; Revised December 21, 2001; Online March 27, 2003
Copyright © 2003 by ASME
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References

Drake, S., 1978, Galileo at Work, His Scientific Biography, University of Chicago Press, Chicago, IL.
Galileo, G., (ca., 1590 and ca. 1600), 1960, On Motion and on Mechanics, The University of Wisconsin Press, Translation by Drakbin and Drake.
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Hacar Benitez, M. A., Bollo, MI. F., and Hacar Rodrigues, M. P., 1977, “Bodies Falling Down on Different Slopes—Dynamic Study,” Proceedings of the 9th International Conference on Soil Mechanics and Foundation Engineering, MAA Publishing, pp. 91–95.
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Keller,  J. B., 1986, “Impact With Friction,” ASME J. Appl. Mech., 53, pp. 1–4.
Wang,  Y., and Mason,  M. T., 1992, “Two-Dimensional Rigid-Body Collisions With Friction,” ASME J. Appl. Mech., 59, pp. 635–642.
Petzold, L. R., 1982, “A Description of DASSL: Differential Algebraic System Solver,” SAND82-8637, Sandia National Laboratories, Sept.
Brenan, K. E., Campbell, S. L., and Petzold, L. R., 1989, Numerical Solution of Initial Value Problems in Differential-Algebraic Equations, Elsevier, New York.
Stoianovici,  D., and Hurmuzlu,  Y., 1996, “A Critical Study of the Applicability of Rigid-Body Collision Theory,” ASME J. Appl. Mech., 63, pp. 307–316.

Figures

Grahic Jump Location
Relation between values of ϕ in subsequent collisions for n=6 and Ω/cos θ=2 (top) and Ω/cos θ=4 (bottom)
Grahic Jump Location
θ=40 deg, μ=0.5,n=100 (top), n=20 (middle), n=10 (bottom) with the dotted line the macroscopic model and the continuous line the numerical calculations. The top and bottom line represent, respectively, perfectly rolling and perfectly sliding
Grahic Jump Location
Effect of the friction coefficient. θ=40 deg,n=20. From top to bottom: μ=0.1,μ=0.4, and μ=0.7, with the dotted line the macroscopic model and the continuous line the numerical calculations.
Grahic Jump Location
Effect of the slope. μ=0.5, n=20. From top to bottom θ=80 deg,θ=50 deg, and θ=20 deg, with the dotted line the macroscopic model and the continuous line the numerical calculations.

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