PMP, (co)adjoint representation, and normal geodesics, of left-invariant (sub-)Finsler metric on Lie groups

Abstract

On the ground of origins of the theory of Lie groups and Lie algebras, their (co)adjoint
representations, and the Pontryagin maximum principle for the time-optimal problem are given
an independent foundation for methods of geodesic vector field to search for normal geodesics
of left-invariant (sub-)Finsler metrics on Lie groups and to look for the corresponding locally
optimal controls in (sub-)Riemannian case, as well as some their applications.