Linearized governing equations are often used in analysis, design, and control applications for dynamical systems. Linearized equations of motion can be formed in either an indirect or direct manner, that is, by first forming or bypassing the full nonlinear equations. Direct linearization is useful for easing the computation of linearized equations, particularly when the full nonlinear equations are not immediately desired. Currently, direct linearization methods derived from a Lagrangian perspective are available. In this paper, these methods are extended to reflect a Gibbs/Appell viewpoint. The resulting directly linearized equations take advantage of features of a Gibbs/Appellian formulation such as the ability to handle nonholonomic constraints and use of quasi-velocities. The Gibbs function and resulting equations are reviewed, the direct linearization method is explained, and a new method for directly linearizing equations via an augmented Gibbs function is presented with examples.
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e-mail: julieparish@tamu.edu
e-mail: jehurtado@tamu.edu
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January 2011
Research Papers
Direct Linearization via the Gibbs Function
Julie J. Parish,
Julie J. Parish
Department of Aerospace Engineering,
e-mail: julieparish@tamu.edu
Texas A&M University
, 3141 TAMU, College Station, TX 77843-3141
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John E. Hurtado
John E. Hurtado
Department of Aerospace Engineering,
e-mail: jehurtado@tamu.edu
Texas A&M University
, 3141 TAMU, College Station, TX 77843-3141
Search for other works by this author on:
Julie J. Parish
Department of Aerospace Engineering,
Texas A&M University
, 3141 TAMU, College Station, TX 77843-3141e-mail: julieparish@tamu.edu
John E. Hurtado
Department of Aerospace Engineering,
Texas A&M University
, 3141 TAMU, College Station, TX 77843-3141e-mail: jehurtado@tamu.edu
J. Comput. Nonlinear Dynam. Jan 2011, 6(1): 011006 (5 pages)
Published Online: September 28, 2010
Article history
Received:
December 15, 2008
Revised:
November 14, 2009
Online:
September 28, 2010
Published:
September 28, 2010
Citation
Parish, J. J., and Hurtado, J. E. (September 28, 2010). "Direct Linearization via the Gibbs Function." ASME. J. Comput. Nonlinear Dynam. January 2011; 6(1): 011006. https://doi.org/10.1115/1.4001906
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