A drift-free left invariant control system on the Lie group \(\mathrm{SO}(3) \times \mathbb R^3 \times \mathbb R^3\) (Q1666255)

Summary: A controllable drift-free system on the Lie group \(G = \mathrm{SO}(3) \times \mathbb R^3 \times \mathbb R^3\) is considered. The dynamics and geometrical properties of the corresponding reduced Hamilton's equations on \(\left(g^{ast}, \left\{\cdot, \cdot\right\}_-\right)\) are studied, where \(\left\{\cdot, \cdot\right\}_-\) is the minus Lie-Poisson structure on the dual space \(g^{\ast}\) of the Lie algebra \(g = so(3) \times \mathbb R^3 \times \mathbb R^3\) of \(G\). The numerical integration of this system is also discussed.