Geodesic
PMP, (co)adjoint representation, and normal geodesics, of left-invariant (sub-)Finsler metric on Lie groups
Čebyševskij sbornik, Tome 21 (2020) no. 2, pp. 43-64

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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 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.
Keywords: (co)adjoint representation, left-invariant (sub-)Finsler metric, left-invariant (sub-)Riemannian metric, Lie algebra, Lie group, mathematical pendulum, normal geodesic, optimal control. 
@article{CHEB_2020_21_2_a5,
     author = {V. N. Berestovskii and I. A. Zubareva},
     title = {PMP, (co)adjoint representation, and normal geodesics, of left-invariant {(sub-)Finsler} metric on {Lie} groups},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {43--64},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2020_21_2_a5/}
}
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V. N. Berestovskii; I. A. Zubareva. PMP, (co)adjoint representation, and normal geodesics, of left-invariant (sub-)Finsler metric on Lie groups. Čebyševskij sbornik, Tome 21 (2020) no. 2, pp. 43-64. http://geodesic.mathdoc.fr/item/CHEB_2020_21_2_a5/