New Approach to the Modeling of Complex Multibody Dynamical Systems

In this paper, a 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, nonautonomous, and possibly yield motions at multiple time and distance scales. These types of problems can easily become difficult to analyze because of the complexity of the equations of motion, which may grow rapidly as the number of component bodies in the multibody system increases. The approach considered herein simplifies the effort required in 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 used to construct the equations of motion of the multibody system. Conceptually, the method relies on a simple three-step procedure. It utilizes the Udwadia–Phohomsiri equation, which describes the explicit equations of motion for constrained mechanical systems with singular mass matrices. The simplicity of the method and its accuracy is illustrated by modeling a multibody spacecraft system.