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TECHNICAL PAPERS

Mechanical Systems With Nonideal Constraints: Explicit Equations Without the Use of Generalized Inverses

[+] Author and Article Information
Firdaus E. Udwadia

Aerospace and Mechanical Engineering, Mathematics, and Information and Operations Management, University of Southern California, Los Angeles, CA 90089 e-mail: fudwadia@usc.edu

Robert E. Kalaba

Electrical Engineering, and Economics, University of Southern California, Los Angeles, CA 90089

Phailaung Phohomsiri

Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089

J. Appl. Mech 71(5), 615-621 (Nov 09, 2004) (7 pages) doi:10.1115/1.1767844 History: Received January 14, 2003; Revised March 08, 2004; Online November 09, 2004
Copyright © 2004 by ASME
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References

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Lagrange, J. L., 1787, Mechanique Analytique, Mme Ve Courcier, Paris.
Udwadia,  F. E., and Kalaba,  R. E., 1992, “A New Perspective on Constrained Motion,” Proc. R. Soc. London, Ser. A, 439, pp. 407–410.
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Udwadia,  F. E., and Kalaba,  R. E., 2001, “Explicit Equations of Motion for Mechanical Systems With Nonideal Constraints,” ASME J. Appl. Mech., 68, pp. 462–467.
Udwadia,  F. E., and Kalaba,  R. E., 2002, “On the Foundations of Analytical Dynamics,” Int. J. Non-Linear Mech., 37, pp. 1079–1090.
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Udwadia,  F. E., 2000, “Fundamental Principles of Lagrangian Dynamics: Mechanical Systems With Non-Ideal, Holonomic, and Non-Holonomic Constraints,” J. Math. Anal. Appl., 252, pp. 341–355.
Udwadia,  F. E., and Kalaba,  R. E., 2002, “What is the General Form of the Explicit Equations of Motion for Constrained Mechanical Systems?” ASME J. Appl. Mech., 69, pp. 335–339.
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Figures

Grahic Jump Location
A bead of mass, m, moving on a circular ring of radius, R
Grahic Jump Location
A block sliding under gravity on an inclined plane (0<α<π/2) that is vibrating vertically with amplitude β and frequency ω. The coefficient of Coulomb friction between the plane and the block is μ.

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