Other multibody formalisms documented in the literature include the studies by Kurdila (Maggie's approach), Keat (velocity transform method). Ho (direct path technique) and Meirovitch (perturbation approach). Jerkovsky presents an excellent overview of the relative merits and disadvantages of selected momentum (Newton-Euler) and velocity (Lagrange) formulations mentioned above. The earlier multibody derivations were based on Newton-Euler approaches. The methods of Newton and Euler are generally recognized as useful in understanding behavior of relatively simple systems, such as particles in space or gyroscopes. However, it is believed that Lagrange gave us superior procedures for deriving equations of motion for complex mechanical systems: it yields the governing equations of motion whose structure is independent of the system geometry. Also, the equations are readily amenable to stability study and well suited for control design. Finally, if equations are to be derived by symbolic processing, the primary criterion for selecting a derivation procedure would be amenability to automation, which encourages reduced dependence on engineering judgment. The pioneering research in multibody dynamics was driven largely by the allure of the equations themselves, and not by the need of computer programs to simulate Spacecraft dynamics being designed at the time. Nowadays, the situation is quite different; the research efforts are governed by the need to develop tools for design and testing of Spacecraft and other systems now committed for development. Several general purpose computer codes aimed at studying dynamics of multibody systems have been commercially available for sometime. They include DISCOS, ALLFLEX, TREETOPS and SD/FAST. These are primarily suitable for systems with large rigid body motion with flexible members undergoing small deformations. Modal Representation Flexible multibody simulation algorithms employ discretization of the continuum based on the classical assumed modes method. This method proposes that the deformation field for each flexible component in the multibody chain can be expressed as a series of spatial and temporal functions. In general, the spatial functions can be any admissible function satisfying geometric boundary conditions and they are often referred to as mode shapes while the corresponding temporal functions are termed generalized coordinates. A daunting task facing dynamicists and control engineers is the choice of modes in discretizing structural deformation. In particular, the focus is on selecting the modes which adequately capture the interaction dynamics involving system parameters, control characteristics and intial disturbances. To establish a framework for selection of modal functions, consider a typical Spacecraft with a rigid hub and elastic appendages. A hierarchy of modes would need to be selected in order to faithfully represent deformation history of the appendages. Either component modes may be used in which the appendages vibrate with respect to the central body but independently of each other; or system modal representation may be performed where the entire structure vibrates accounting for dynamical interactions throughout the Spacecraft. The 'component modes' method was pioneered by Hurty in the early 1960's. It involves determination of the appendage admissible functions with enforced geometric compatibility between the adjacent elements of the system. Since temporal generalized coordinates are associated with each mode for a given component, the size of the problem is directly dependent on the number of appendages and modes. Another drawback of this method is in die development of a dynamically faithful set of admissible functions for geometrically complex structures with interconnected flexible components. Further investigations on modal selection by Craig and Bampton, Benfield and Hruda and Hughes were aimed at improving modal convergence by more precise specification of geometric conditions at internal boundaries between the substructures. On the other hand, with ‘system modes', frequently obtained by the finite element method, the size of the problem is independent of the geometric complexity of the structure. The study by Hablani suggests that, for a given order of discretization, prediction of the Spacecraft's dynamics improves as one migrates from the component to the system modes. Furthermore, system modes are physically more meaningful, since a modal frequency represents resonance of the the entire structure. Another important issue is to model accurately a flexible lattice structure. For example, in the case of the Space Station, should the truss structure be considered homogeneous, and if so, how? Design of the lattice structure, which constitutes the main truss, must be highly reliable since it cannot be tested full scale in its operational environment prior to the flight. On the other hand, a detailed finite element analysis of the truss structure using truss bar elements would involve a
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