A Projection Method Approach to Constrained Dynamic Analysis

[+] Author and Article Information
W. Blajer

Institute B of Mechanics, University of Stuttgart, Pfaffenwaldring 9, 7000 Stuttgart 80, Germany

J. Appl. Mech 59(3), 643-649 (Sep 01, 1992) (7 pages) doi:10.1115/1.2893772 History: Received August 01, 1990; Revised December 17, 1990; Online March 31, 2008


The paper presents a unified approach to the dynamic analysis of mechanical systems subject to (ideal) holonomic and/or nonholonomic constraints. The approach is based on the projection of the initial (constraint reaction-containing) dynamical equations into the orthogonal and tangent subspaces; the orthogonal subspace which is spanned by the constraint vectors, and the tangent subspace which complements the orthogonal subspace in the system’s configuration space. The tangential projection gives the reaction-free (or purely kinetic) equations of motion, whereas the orthogonal projection determines the constraint reactions. Simplifications due to the use of independent variables are indicated, and examples illustrating the concepts are included.

Copyright © 1992 by The American Society of Mechanical Engineers
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