What is the General Form of the Explicit Equations of Motion for Constrained Mechanical Systems?

[+] Author and Article Information
F. E. Udwadia

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

R. E. Kalaba

University of Southern California, Los Angeles, CA 90089

J. Appl. Mech 69(3), 335-339 (May 03, 2002) (5 pages) doi:10.1115/1.1459071 History: Accepted April 18, 2000; Online May 03, 2002
Copyright © 2002 by ASME
Your Session has timed out. Please sign back in to continue.


Lagrange, J. L., 1787, Mecanique Analytique, Mme Ve Courcier, Paris.
Gauss,  C. F., 1829, “Uber Ein Neues Allgemeines Grundgesetz der Mechanik,” J. Reine Agnew. Math., 4, pp. 232–235.
Gibbs,  J. W., 1879, “On the Fundamental Formulas 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.
Poincare,  H., 1901, “Sur une forme nouvelle des equations de la mecanique,” C. R. Acad. Sci., Paris, 132, pp. 369–371.
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.
Moore,  E. H., 1920, “On the Reciprocal of the General Algebraic Matrix,” Bull. Am. Math. Soc., 26, pp. 394–395.
Penrose,  R., 1955, “A Generalized Inverse of Matrices,” Proc. Cambridge Philos. Soc., 51, pp. 406–413.
Goldstein, H., 1981, Classical Mechanics, Addison-Wesley, Reading, MA.
Pars, L. A., 1979, A Treatise on Analytical Dynamics, Oxbow Press, Woodridge, CT.
Udwadia,  F. E., and Kalaba,  R. E., 2000, “Non-ideal Constraints and Lagrangian Dynamics,” Journal of Aerospace Engineering, 13, Jan., pp. 17–22.
Udwadia,  F. E., and Kalaba,  R. E., 2001, “Explicit Equations of Motion for Systems With Non-ideal Constraints,” ASME J. Appl. Mech. , 68, pp. 462–467.
Udwadia,  F. E., 2000, “Fundamental Principles and Lagrangian Dynamics: Mechanical Systems With Non-ideal, Holonomic, and Nonholonomic Constraints,” J. Math. Anal. Appl., 251, pp. 341–355.
Udwadia, F. E., and Kalaba, R. E., 1996, Analytical Dynamics: A New Approach, Cambridge University Press, England.




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In