| One of the goals of multibody dynamic research is to automatically generate the governing equations of motion for a given system. To this end, several symbolic and numeric formulations have been developed that systematically produce equations that describe the motion of a system, given only a description of the system's components and the interconnections between them (topology). However, few of these formulations accommodate components from non-mechanical energy domains (electric, hydraulic, pneumatic, etc.), and they are often restricted to joint or absolute coordinates. Even fewer provide any systematic method for generating new symbolic components out of subsystems of interconnected, simpler components.; To this end, the contributions of this thesis help facilitate the efficient formulation of symbolic equations for multibody, multi-domain systems. In particular, this thesis presents an extended linear graph component template that allows components to contain internal variables and equations. A new linear graph formulation, based upon the principle of orthogonality, accommodates this component template in the generation of a system's governing symbolic equations. Since the formulation is rooted in linear graph theory, all of the advantages inherent in a graph-theoretic approach (e.g. multi-domain, allows modelling variable selection, systematic) are achieved. Finally, using this formulation and component template, a method to automatically generate a new subsystem component (derived from multiple interconnected components) is also presented. Since the subsystem components are generated symbolically, they can be stored in a library for future use.; The ability to formulate and store the equations for a portion of a system allows the governing symbolic equations for complicated multibody, multi-domain systems to be formulated in a piecewise fashion. First, the equations governing the identified subsystems are generated, followed by the generation of the equations for the overall system. Such an approach results in decreased formulation times when repeated subsystems or parallel processing facilities are present. Additionally, since the symbolic equations are formulated, the approach can generate efficient simulation code (including trigonometric substitutions, symbolic simplifications, removal of multiplications by 1's and 0's) for the analysed system.; To validate the above theory, a body of software---DynaFlexPro---has been created. Although the software, written in Maple 9.5, does not constitute a theoretical contribution, its scope and functionality merits its inclusion as a contribution of this research. |
