Coordinate Reduction in the Dynamics of Constrained Multibody Systems—A New Approach

[+] Author and Article Information
S. K. Ider, F. M. L. Amirouche

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

J. Appl. Mech 55(4), 899-904 (Dec 01, 1988) (6 pages) doi:10.1115/1.3173739 History: Received October 15, 1987; Revised April 28, 1988; Online July 21, 2009


In this paper a new theorem for the generation of a basis for the null space of a rectangular matrix, with m linearly independent rows and n (n > m) columns is presented. The method is based on Gaussian row operations to transform the constraint Jacobian matrix to an uptriangular matrix. The Gram-Schmidt process is then utilized to identify basis vectors orthogonal to the uptriangular matrix. A complement orthogonal array which forms the basis for the null space for which the algebraic constraint equations are satisfied is then formulated. An illustration of the theorem application to constrained dynamical systems for both Lagrange and Kane’s equations is given. A numerical computer algorithm based on Kane’s equations with embedded constraints is also presented. The method proposed is well conditioned and computationally efficient and inexpensive.

Copyright © 1988 by ASME
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