RESEARCH PAPERS: Design Automation Papers

A Variational-Vector Calculus Approach to Machine Dynamics

[+] Author and Article Information
E. J. Haug, M. K. McCullough

Department of Mechanical Engineering and Center for Computer Aided Design, College of Engineering, The University of Iowa, Iowa City, Iowa 52242

J. Mech., Trans., and Automation 108(1), 25-30 (Mar 01, 1986) (6 pages) doi:10.1115/1.3260779 History: Received June 12, 1985; Online November 19, 2009


A variational-vector calculus approach is presented to define virtual displacements and rotations and position, velocity, and acceleration of individual components of a multibody mechanical system. A two-body subsystem with both Cartesian and relative coordinates is used to illustrate a systematic method of exploiting the linear structure of both vector and differential calculus, in conjunction with a variational formulation of the equations of motion of rigid bodies, to derive the matrix structure of governing multibody system equations of motion. A pattern for construction of the system mass matrix and generalized force terms is developed and applied to derivation of the equations of motion of a vehicle system. The development demonstrates an approach to multibody machine dynamics that closely parallels methods used in finite-element structural analysis.

Copyright © 1986 by ASME
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