Journal of Applied Mathematics
Volume 2012 (2012), Article ID 341470, 14 pages
Research Article

An Underactuated Drift-Free Left Invariant Control System on a Specific Lie Group

Math Department, “Politehnica” University of Timişoara, Piaţa Victoriei No. 2, 300006 Timişoara, Romania

Received 25 August 2011; Revised 8 November 2011; Accepted 9 November 2011

Academic Editor: Chein-Shan Liu

Copyright © 2012 Camelia Pop Arieşanu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The paper presents a geometrical overview on an optimal control problem on a special Lie group. The Hamilton-Poisson realization of the dynamics offers us the possibility to study the system from mechanical geometry point of view.