A New General Method for Modeling Complex Multibody Dynamical Systems

Abstract

In this paper, a new general method for modeling complex multibody systems is presented. The method utilizes recent results in analytical dynamics adapted to general complex multibody systems. The term complex is employed to denote those multibody systems whose equations of motion are highly nonlinear, non-autonomous, and possibly yield motions at multiple time and distance scales. The approach considered herein opens up new routes for modeling general multibody systems by explicitly developing closed form expressions in terms of any desirable number of generalized coordinates that may appropriately describe the configuration of the multibody system. Furthermore, the approach is simple in implementation because it poses no restrictions on the total number and nature of modeling constraints required to construct the equations of motion of the multibody system. Conceptually, the method relies on a simple three-step procedure. It utilizes a new set of equations of motion developed by Udwadia and Schutte, which describes the explicit equations of motion for constrained mechanical systems with singular mass matrices. The simplicity of the method is highlighted by illustrating its use in the modeling of a multibody spacecraft system for which we provide numerical results of the system's response.