Base-controlled mechanical systems and geometric phases

Details Base-controlled mechanical systems and geometric phases Base-controlled mechanical systems and geometric phases

2007-06-11

arxiv.org/abs/0706.1545v1

Physics

Mathematical Physics

44 pages, 1 figure

Scientific paper

10.1016/j.geomphys.2007.11.009

In this paper, we carry a detailed study of mechanical systems with configuration space $Q\longrightarrow Q/G$ for which the base $Q/G$ variables are being controlled. The overall system's motion is considered to be induced from the base one due to the presence of general non-holonomic constraints. It is shown that the solution can be factorized into dynamical and geometrical parts. Moreover, under favorable kinematical circumstances, the dynamical part admits a further factorization since it can be reconstructed from an intermediate (body) momentum solution, yielding a reconstruction phase formula. Finally, we apply this results to the study of concrete mechanical systems.

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