The Maggi or Canonical Form of Lagrange’s Equations of Motion of Holonomic Mechanical Systems

[+] Author and Article Information
John G. Papastavridis

School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332

J. Appl. Mech 57(4), 1004-1010 (Dec 01, 1990) (7 pages) doi:10.1115/1.2897618 History: Received December 21, 1988; Revised June 22, 1989; Online March 31, 2008


This paper formulates the simplest possible, or canonical, form of the Lagrangean-type of equations of motion of holonomically constrained mechanical systems. This is achieved by introducing a new special set of n holonomic (system) coordinates in terms of which the m ( < n) holonomic constraints are expressed in their simplest, or uncoupled, form: the first m of these new coordinates vanish; the remaining (n-m) (nonvanishing) new coordinates of the (n-m) degree-of-freedom system are then independent. From the resulting equations of motion: (a) The last (n-m) are reactionless canonical equations (the holonomic counterpart of the linear or nonlinear equations, either of Maggi (in the old variables), or of Boltzmann/Hamel (in the new variables)) whose solution yields the motion, while (b) the first m supply the system reactions, in the old or new coordinates, once the motion is known. Special forms of these equations and a simple example are also given. The geometrical interpretation of the above, in modern vector/linear algebra language is summarized in the Appendix.

Copyright © 1990 by The American Society of Mechanical Engineers
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