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RESEARCH PAPERS: Design Automation Papers

Generalized Coordinate Partitioning for Analysis of Mechanical Systems with Nonholonomic Constraints

[+] Author and Article Information
P. E. Nikravesh, E. J. Haug

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

J. Mech., Trans., and Automation 105(3), 379-384 (Sep 01, 1983) (6 pages) doi:10.1115/1.3267371 History: Received June 11, 1982; Online November 19, 2009

Abstract

This paper presents a computer-based method for formulation and efficient solution of nonlinear, constrained differential equations of motion for spatial dynamic analysis of mechanical systems with holonomic and nonholonomic constraints. Holonomic and nonholonomic constraint equations and differential equations of motion are written in terms of a maximal set of Cartesian generalized coordinates, three translational and four rotational coordinates for each rigid body in the system, where the rotational coordinates are Euler parameters. The maximal set of generalized coordinates facilitates the general formulation of constraints and forcing functions. A Gaussian elimination algorithm with full pivoting decomposes the constraint Jacobian matrix and identifies independent coordinates and velocities. This information is employed to numerically construct a reduced system of differential equations of motion whose solution yields the system dynamic response. A numerical integration algorithm with positive-error control, employing a predictor-corrector algorithm with variable order and step size, integrates for only the independent variables, yet effectively determines dependent variables.

Copyright © 1983 by ASME
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