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TECHNICAL PAPERS

Explicit Equations of Motion for Mechanical Systems With Nonideal Constraints

[+] Author and Article Information
F. E. Udwadia, R. E. Kalaba

University of Southern California, Los Angeles, CA 90089-1453

J. Appl. Mech 68(3), 462-467 (Oct 09, 2000) (6 pages) doi:10.1115/1.1364492 History: Received April 02, 2000; Revised October 09, 2000
Copyright © 2001 by ASME
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References

Lagrange, J. L., 1787, Mecanique Analytique, Mme Ve Courcier, Paris.
Gauss,  C. F., 1829, “Uber Ein Neues Allgemeines Grundgesetz der Mechanik,” J. Reine Ang. Math.,, 4, pp. 232–235.
Gibbs,  J. W., 1879, “On the Fundamental Formulae of Dynamics,” Am. J. Math., 2, pp. 49–64.
Appell,  P., 1899, “Sur une Forme Generale des Equations de la Dynamique,” C. R. Acad. Sci., Paris,, 129, pp. 459–460.
Pars, L. A., 1979, A treatise on Analytical Dynamics, Oxbow Press, Woodridge, CT, p. 202.
Dirac, P. A. M., 1964, Lectures in Quantum Mechanics, Yeshiva University, New York.
Udwadia,  F. E., and Kalaba,  R. E., 1992, “A New Perspective on Constrained Motion,” Proc. R. Soc. London, Ser. A, 439, pp. 407–410.
Udwadia, F. E., and Kalaba, R. E., 1996, Analytical Dynamics: A New Approach, Cambridge University Press, Cambridge, UK.
Goldstein, H., 1981, Classical Mechanics, Addison-Wesley, Reading, MA.
Udwadia,  F. E., and Kalaba,  R. E., 2000, “Non-ideal Constraints and Lagrangian Dynamics,” J. Aerosp. Eng.,, 13, pp. 17–22.
Penrose,  R., 1955, “A Generalized Inverse of Matrices,” Proc. Cambridge Philos. Soc., 51, pp. 406–413.
Udwadia,  F. E., and Kalaba,  R. E., 1995, “The Geometry of Constrained Motion,” Z. Angew. Math. Mech., 75, pp. 637–640.

Figures

Grahic Jump Location
The geometry of constrained motion is depicted using projections on N(B) and R(BT). The projection of q̈s on N(B) is the same as that of (as+cs) because Nq̈s=N(as+cs). The vector B+b is orthogonal to this projection.

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