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Research Papers

Direct Linearization via the Gibbs Function

[+] Author and Article Information
Julie J. Parish1

Department of Aerospace Engineering, Texas A&M University, 3141 TAMU, College Station, TX 77843-3141julieparish@tamu.edu

John E. Hurtado

Department of Aerospace Engineering, Texas A&M University, 3141 TAMU, College Station, TX 77843-3141jehurtado@tamu.edu

1

Corresponding author.

J. Comput. Nonlinear Dynam 6(1), 011006 (Sep 28, 2010) (5 pages) doi:10.1115/1.4001906 History: Received December 15, 2008; Revised November 14, 2009; Published September 28, 2010; Online September 28, 2010

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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Figures

Grahic Jump Location
Figure 1

The sled can move forward or rotate but cannot move side to side

Grahic Jump Location
Figure 2

The coordinate frame b is body-fixed to the complex spacecraft

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