A Recursive Householder Transformation for Complex Dynamical Systems With Constraints

[+] Author and Article Information
F. M. L. Amirouche, Tongyi Jia, Sitki K. Ider

Department of Mechanical Engineering, University of Illinois at Chicago, Chicago, Ill. 60680

J. Appl. Mech 55(3), 729-734 (Sep 01, 1988) (6 pages) doi:10.1115/1.3125857 History: Received January 08, 1987; Revised February 01, 1988; Online July 21, 2009


A new method is presented by which equations of motion of complex dynamical systems are reduced when subjected to some constraints. The method developed is used when the governing equations are derived using Kane’s equations with undetermined multipliers. The solution vectors of the constraint equations are determined utilizing the recursive Householder transformation to obtain a Pseudo-Uptriangular matrix. The most general solution in terms of new independent coordinates is then formulated. Methods previously used for handling such systems are discussed and the new method advantages are illustrated. The procedures developed are suitable for computer automation and especially in developing generic programs to study a large class of systems dynamics such as robotics, biosystems, and complex mechanisms.

Copyright © 1988 by ASME
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