Dynamics Theory And Application Research Of Chained Multibody System Based On The Representation Of Adjoint Operator

The ideas and methods of modern differential geometry have found wide application in classical mechanics, in the theory of multibody system dynamics, and in the Lagrangian and Hamiltonian formalisms of mechanics. In general, modern differential geometry includes the Lie group, Lie algebra, Riemannian manifolds and Symplectic manifolds etc. On which multibody system dynamics formulations describe the multibody behavior at a very high level of abstraction and clearly have obvious physical interpretations. The numerical precision and formulation efficiency of multibody system dynamics directly depend on the choosing the local frame coordinates and global coordinate, and on the formulation methods. So it becomes a significant subject how to improve the efficiency of multibody system dynamics formulations and a lot of researchers working on dynamics pay much attention and resource to the research. In the 90s of the last century American scientists G. Rodriguez and A.Jain et al developed a new spatial operator algebra which is a theory for a concise and systematic formulation of the dynamical equations of motion of multibody systems and the efficient computational recursive algorithms. The theory is widely used in many areas of engineering: aerospace, automobiles, machinery, robotics , biomechanics, etc. and resolves many difficult issues for complex multibody systems dynamic analysis, design and simulation in engineering areas. Therefore, it is worth to deeply investigate and perfect the spatial operator algebra. In this thesis the research comes from the spatial operator algebra, the theories are investigated in a high level. It establishes the efficient and precise equations for multibody system dynamics in the field of the Lie group, Lie algebra, Riemannian manifolds in terms of the adjoint transformation so that to prove these theories and methods are very significant . Our main research work is as following: We completely and systematically review the development course of multibody systems dynamics and expatiate the homology and differentia between the dynamics formulations of multibody systems, the advantages of these dynamics formulations to the various complex multibody systems. Specify what status the spatial operator algebra locates at in many methods of multibody systems dynamics formulations and what the relations are between the spatial operator algebra and other dynamics formulations.We explain the basic conception of the Lie group, Lie algebra and Riemannian manifolds in detail, deeply analyze and research the Special Euclidean Group SE(3) and se(3) in the Lie group, Lie algebra. Establish the relation between the adjoint transformation Adg and the operatorφ(k + 1,k) under a particular condition, substitute the operatorφ(k + 1,k)with spatial adjoint operator Ad kk ?1 to establish the dynamic equations on the Riemannian manifolds. Deeply study the relationship between the Riemannian metric and the adjoint operator Ad kk ?1 and present the objective map expressions. Develop the formulation of the the Lie group, Lie algebra and Riemannian manifolds and spatial operator algebra.