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TECHNICAL PAPERS

On the Simulation of Discontinuous Functions

[+] Author and Article Information
J. D. Turner

National Advanced Driving Simulator and Simulation Center, The University of Iowa, 2401 Oakdale Boulevard, Iowa City, IA 52242-5003e-mail: jturner@nads-sc.uiowa.edu

J. Appl. Mech 68(5), 751-757 (Apr 16, 2001) (7 pages) doi:10.1115/1.1387022 History: Received July 12, 2000; Revised April 16, 2001
Copyright © 2001 by ASME
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References

Carver,  M. B., 1978, “Efficient Integration Over Discontinuities in Ordinary Differential Equation Simulations,” Math. Comput. Simul., 20, No. 3, pp. 190–196.
Ellison,  D., 1981, “Efficient Automatic Integration Of Odes With Discontinuities,” Math. Comput. Simul., 23, No. 1, pp. 12–20.
Enright,  W. H., Jackson,  K. R., Nørsett,  S. P., and Thomson,  P. G., 1986, “Effective Solution of Discontinuous Ivps Using a Runge-Kutta Formula Pair With Interpolants,” Appl. Math. Comput., 27, pp. 313–335.
Filippov,  A. F., 1964, “Differential Equations With Discontinuous Right Hand Side,” ASM Trans. 42, pp. 199–231.
Halin, H. J., 1976, “Integration of Ordinary Differential Equations Containing Discontinuities,” Proceedings of the Summer Computer Simulation Conference 976, La Jolla, SCI Press, La Jolla, CA, pp. 46–53.
Pfeiffer,  F., 1984, “Mechanische Systeme mit unstetigen Übergängen,” Ingenieurarchiv, 54, pp. 232–240.
Eich-Soellner, Edda, and Fuhrer, Claus, 1998, Numerical Methods in Multibody Dynamics, B. G. Teubner, Stuttgart.
Hildbrand, F. B., 1962, Advanced Calculus for Applications, Prentice-Hall, Englewood Cliffs, NJ.

Figures

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Discontinuous model motion phases
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(a) State variable discontinuity, (b) smoothed state variable discontinuity
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Discontinuity detected in the time interval and slack variable initial condition
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Flow diagram for the slack variable integration algorithm
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Phase variable plot for woodpecker angle-angular rate plot
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Woodpecker angle time history
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Woodpecker angular rate time history
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Woodpecker height on rod
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Woodpecker translational velocity relative to the rod
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Nonlinear phase motion time history
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Model degree-of-freedom time history

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