In this paper we develop results based on geometric mechanics to study the controllability of a class of controlled under-actuated left invariant mechanical systems on Lie groups....
: Linear integral operators describing physical problems on symmetric domains often are equivariant, which means that they commute with certain symmetries, i.e., with a group of or...
— Lie group symmetry in a mechanical system can lead to a dimensional reduction in its dynamical equations. Typically, the symmetries that one exploits are intrinsic to the mecha...