In this paper we obtain the explicit equations of motion for mechanical systems under nonideal constraints without the use of generalized inverses. The new set of equations is shown to be equivalent to that obtained using generalized inverses. Examples demonstrating the use of the general equations are provided.
Issue Section:
Technical Papers
Topics:
Equations of motion
1.
Appell
, P.
, 1899
, “Sur une Forme Generale des Equations de la Dynamique
,” C. R. Acad. Sci., Paris
, 129
, pp. 459
–460
.2.
Beghin, H., 1967, Mecanique Theorique et Appliquee, Gauthier-Villars, Paris.
3.
Chetaev, N. G., 1989, Theoretical Mechanics, Mir Publisher, Moscow.
4.
Dirac, P. A. M., 1964, Lectures in Quantum Mechanics, Yeshiva University, New York.
5.
Gauss
, C. F.
, 1829
, “Uber Ein Neues Allgemeines Grundgsetz der Mechanik
,” J. Reine Angew. Math.
, 4
, pp. 232
–235
.6.
Gibbs
, J. W.
, 1879
, “On the Fundamental Formulas of Dynamics
,” Am. J. Math.
, 2
, pp. 49
–64
.7.
Hamel, P. G., 1949, Theoretische Mechanik: Eine Einheitliche Einfuhrung in die Gesamte Mechanik, Springer-Verlag, Berlin.
8.
Lagrange, J. L., 1787, Mechanique Analytique, Mme Ve Courcier, Paris.
9.
Udwadia
, F. E.
, and Kalaba
, R. E.
, 1992
, “A New Perspective on Constrained Motion
,” Proc. R. Soc. London, Ser. A
, 439
, pp. 407
–410
.10.
Pars, L. A., 1979, A Treatise on Analytical Dynamics, Oxbow Press, Woodridge, CT, p. 14.
11.
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
.12.
Udwadia
, F. E.
, and Kalaba
, R. E.
, 2002
, “On the Foundations of Analytical Dynamics
,” Int. J. Non-Linear Mech.
, 37
, pp. 1079
–1090
.13.
Udwadia, F. E., and Kalaba, R. E., 1996, Analytical Dynamics: A New Approach, Cambridge University Press, Cambridge, UK.
14.
Udwadia
, F. E.
, Kalaba
, R. E.
, and Hee-Chang
, E.
, 1997
, “Equation of Motion for Constrained Mechanical Systems and The Extended D’Alembert’s Principle
,” Q. Appl. Math.
, LV
(2
), pp. 321
–331
.15.
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
.16.
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
.17.
Synge
, J. L.
, 1927
, “On the Geometry of Dynamics
,” Philos. Trans. R. Soc. London, Ser. A
, 226
, pp. 31
–106
.18.
Bowden, F. P., and Tabor, D., 1974, Friction: An Introduction to Tribology, Heinemann, London.
19.
Moore
, E. H.
, 1920
, “On the Reciprocal of The General Algebraic Matrix
,” Bull. Am. Math. Soc.
, 26
, pp. 394
–395
.20.
Penrose
, R.
, 1955
, “A Generalized Inverse of Matrices
,” Proc. Cambridge Philos. Soc.
, 51
, pp. 406
–413
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