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TECHNICAL PAPERS

A New Look at an Old Problem: Newton’s Cradle

[+] Author and Article Information
V. Ceanga, Y. Hurmuzlu

Mechanical Engineering Department, Southern Methodist University, Dallas, TX 75275

J. Appl. Mech 68(4), 575-583 (Apr 16, 2000) (9 pages) doi:10.1115/1.1344902 History: Received September 15, 1999; Revised April 16, 2000
Copyright © 2001 by ASME
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References

Marghitu,  D. B., and Hurmuzlu,  Y., 1995, “Three-Dimensional Rigid-Body Collisions With Multiple Contact Points,” ASME J. Appl. Mech., 62, pp. 725–732.
Johnson,  W., 1976, “Simple Linear Impact,” ImechE. IJMEE, 4, No. 2, pp. 167–181.
Han,  I., and Gilmore,  B. J., 1993, “Multi-Body Impact Motion With Friction—Analysis, Simulation, and Experimental Validation,” ASME J. Mech. Des., 115, pp. 412–422.
Brogliato, B., 1996, Nonsmooth Impact Mechanics: Models, Dynamics and Control, Springer-Verlag, New York, LNCIS 220.
Smith,  E. A. L., 1955, “Impact and Longitudinal Wave Transmission,” Trans. ASME, 77, pp. 963–973.
Walkiewicz,  T. A., and Newby,  N. D., 1972, “Linear Collisions,” Am. J. Phys., 40, pp. 133–137.
Newby,  N. D., 1979, “Linear Collisions With Harmonic Oscillator Forces: The Inverse Scattering Problem,” Am. J. Phys., 47, No. 2, pp. 161–165.
Hinch,  E. J., and Saint-Jean,  S., 1999, “The Fragmentation of a Line of Balls by an Impact,” Proc. R. Soc. London, Ser. A, 455, pp. 3201–3220.
Cholet, C., 1998, “Chocs de Solids Rigid,” Ph.D. thesis, University of Paris 6 and LCPC-CNRS.
Moreau,  J. J., 1994, “Some Numerical Methods in Multibody Dynamics: Application to Granular Materials,” Eur. J. Mech. A/Solids, 13, No. 4, pp. 93–114.
Fremond,  M., 1995, “Rigid Bodies Collisions,” Phys. Lett. A, 204, pp. 33–41.
Stronge,  W. J., 1990, “Rigid Body Collisions with Friction,” Proc. R. Soc. London, Ser. A, 431, pp. 169–181.

Figures

Grahic Jump Location
The compliant, three-ball chain
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Velocity-impulse graphs
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Effect of α on the post impact velocities
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Multiple impacts on the velocity-impulse diagram
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Bouncing pattern regions on the r1–r2 plane
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Velocity-impulse diagram of a small center-ball example
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Intermittent collisions
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The experimental set-up
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Velocity predictions in four ball experiments
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Velocity predictions in sequences with the heavy balls
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Velocity predictions in five and six ball experiments

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