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Shock and Vibration
Volume 1 (1993), Issue 2, Pages 107-119

Derivation of Equations for Flexible Multibody Systems in Terms of Quasi-Coordinates from the Extended Hamilton’s Principle

L. Meirovitch

Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA

Copyright © 1993 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Early derivations of the equations of motion for single rigid bodies, single flexible bodies, and flexible multibody systems in terms of quasi-coordinates have been carried out in two stages. The first consists of the use of the extended Hamilton’s principle to derive standard Lagrange’s equations in terms of generalized coordinates and the second represents a transformation of the Lagrange’s equations to equations in terms of quasi-coordinates. In this article, hybrid (ordinary and partial) differential equations for flexible multibody systems are derived in terms of quasi-coordinates directly from the extended Hamilton's principle. The approach has beneficial implications in an eventual spatial discretization of the problem.