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Differential-Geometric Characteristics of Optimized Generalized Coordinates Partitioned Vectors for Holonomic and Non-Holonomic Multibody Systems

Differential-geometric characteristics and structure of optimized generalized coordinates partitioned vectors for generally constrained multibody systems are discussed. Generalized coordinates partitioning is well-known procedure that can be applied in the framework of numerical integration of DAE systems. However, although the procedure proves to be a very useful tool, it is known that an optimization algorithm for coordinates partitioning is needed to obtain the best performance. After short presentation of differential-geometric background of optimized coordinates partitioning, the structure of optimally partitioned vectors is discussed on the basis of gradient analysis of separate constraint sub-manifolds at configuration and velocity level when holonomic and non-holonomic constraints are present in the system. While, in the case of holonomic systems, the vectors of optimally partitioned coordinates have the same structure for generalized positions and velocities, when non-holonomic constraints are present in the system, the optimally partitioned coordinates generally differ at configuration and velocity level and separate partitioned procedure has to be applied. The conclusions of the paper are illustrated within the framework of the presented numerical example.

Multibody dynamics; Numerical Integration; Coordinates partitioning; Manifolds

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