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

Pontryagin maximum principle, (co)adjoint representation, and normal geodesics of left-invariant (sub-)Finsler metrics on Lie groups