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Adjoint transformations and adjoint operators of Lie groups and Lie algebra are discussed in this paper to study the recursive dynamics of complex systems. The dynamics based on Lie groups and Lie algebra of tree topology systems is then developed. Efficient dynamics algorithms for closed-loop systems and flexible systems can be developed. Simulation results show that the dynamic problems can be solved quickly and efficiently using the method. This study provides a foundation for real-time control based on dynamics

Dynamics of Complex Mechanical Systems Based on Lie Groups and Lie algebra