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.
"An Underactuated Drift-Free Left Invariant Control System on a Specific Lie Group." J. Appl. Math. 2012 1 - 14, 2012. https://doi.org/10.1155/2012/341470