| In order to simulate the behavior of complicated spacecraft, a branch of dynamics, known as multibody dynamics, was developed in the 1960's. This theory allowed the analysis of a variety of structures to be examined in a procedural way rather than with specific derivation of the equations of motion. Certain types of spacecraft undergo articulation of flexible appendages, which presents a complicated form of the nonlinear dynamics problem. The ideas in this dissertation are presented in a manner that attempts to link the concepts of component mode selection and component frame selection in flexible multibody dynamic systems.;Four separate ideas are presented in this dissertation. First, a new mode set is introduced for the use of characterizing flexibility in multibody dynamics. The Generalized Hurty Coordinate Set is analogous to the linear Component Mode Synthesis coordinate set proposed by Hurty in the 1960's. It is shown that use of this coordinate set distinguishes between rotational and translational rigid-body coordinates, and is complemented by redundant constraint modes and fixed-interface vibration modes. Second, the secant component reference frame is described. This concept has been previously introduced in the literature but it is expanded in this dissertation beyond the scope of the original formulation. This dissertation also discusses the importance of component reference frames in the development of system kinematics.;Third, the consistent-mass and lumped-mass multibody formulations are contrasted. These two methods are derived from linear structural dynamics and are used to generate mass and stiffness matrices for various components. Most multibody formulations in the literature incorporate the lumped-mass approach, which assumes that finite element mass is concentrated at node points. The consistent-mass approach works under the assumption that a continuum exists between finite element node points and takes advantage of this assumption in the multibody formulation. The results of these two formulations are contrasted by means of a simple example.;Finally, the concept of third-order tensors for use in flexible multibody dynamics is discussed. A third-order tensor results from the differentiation of a matrix by a vector. Use of the third-order tensor in the multibody dynamics formulation simplifies much of the nomenclature and bookkeeping in this problem. |
