Direct Linearization via the Gibbs Function

Abstract

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.