English

Base-controlled mechanical systems and geometric phases

Mathematical Physics 2009-11-13 v1 Differential Geometry math.MP

Abstract

In this paper, we carry a detailed study of mechanical systems with configuration space QQ/GQ\longrightarrow Q/G for which the base Q/GQ/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.

Keywords

Cite

@article{arxiv.0706.1545,
  title  = {Base-controlled mechanical systems and geometric phases},
  author = {Alejandro Cabrera},
  journal= {arXiv preprint arXiv:0706.1545},
  year   = {2009}
}
R2 v1 2026-06-21T08:37:18.684Z