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
Voir la notice de l'article provenant de la source Math-Net.Ru
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/}
}
TY - JOUR AU - V. N. Berestovskii AU - I. A. Zubareva TI - PMP, (co)adjoint representation, and normal geodesics, of left-invariant (sub-)Finsler metric on Lie groups JO - Čebyševskij sbornik PY - 2020 SP - 43 EP - 64 VL - 21 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/CHEB_2020_21_2_a5/ LA - en ID - CHEB_2020_21_2_a5 ER -
%0 Journal Article %A V. N. Berestovskii %A I. A. Zubareva %T PMP, (co)adjoint representation, and normal geodesics, of left-invariant (sub-)Finsler metric on Lie groups %J Čebyševskij sbornik %D 2020 %P 43-64 %V 21 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/CHEB_2020_21_2_a5/ %G en %F CHEB_2020_21_2_a5
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/