Linearization approaches for general multibody systems validated through stability analysis of a benchmark bicycle model

Linearizing the equations of motion of a constrained multibody system is a common need in, for example, stability analyses. While the theory of modelling multibody systems is well developed and many references in the literature include formalisms to generate the nonlinear equations of motion, to the best of the authors' knowledge the linearization of those equations has not been detailed in a general procedure that could be applied to any kind of holonomic or nonholonomic multibody system. The literature includes examples of linearized equations of motion of multibody systems based on symbolic computation. Nevertheless, symbolic computation is not an option when the multibody system model is sufficiently large in terms of equations and coordinates. Efficiency of the linearization procedures has not been an issue so far since symbolic computation of the linearized equations results in very cumbersome mathematical expressions, which in some cases cannot be handled by today's personal computers. In this paper, different numerical approaches to perform the linearization of the equations of motion of general multibody systems are developed. To validate the proposed procedures, a well-acknowledged benchmark bicycle model has been used. According to the results, the numerical linearization procedures are completely general, more efficient and very accurate.