On the Linearization of Multibody Dynamics Formulations

The dynamics equations of multibody systems are often expressed in the form of a system of highly nonlinear Differential Algebraic Equations (DAEs). Some applications of multibody dynamics, however, require a linear expression of the equations of motion. Such is the case of the plant representations demanded by a wide variety of control algorithms and the system models needed by state estimators like Kalman filters. The choice of generalized coordinates used to describe a mechanical system greatly influences the behavior of the resultant linearized models and the way in which they convey information about the original system dynamics. Several approaches to arrive at the linearized dynamics equations have been proposed in the literature. In this work, these were categorized into three major groups, defined by the way in which the kinematic constraints are handled. The properties of each approach and the differences between them were studied through the linearization of the dynamics of a simple example with a method representative of each class.