Second order Lagrangian dynamics on double cross product groups

We observe that the iterated tangent group of a Lie group may be realized as a double cross product of the 2nd order tangent group, with the Lie algebra of the base Lie group. Based on this observation, we derive the 2nd order Euler–Lagrange equations on the 2nd order tangent group from the 1st orde...

Full description

Saved in:
Bibliographic Details
Published in:Journal of geometry and physics 2021-01, Vol.159, p.103934, Article 103934
Main Authors: Esen, Oğul, Kudeyt, Mahmut, Sütlü, Serkan
Format: Article
Language:English
Subjects:
Euler–Poincaré equation
Matched pairs of Lie groups
Second order tangent bundles
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We observe that the iterated tangent group of a Lie group may be realized as a double cross product of the 2nd order tangent group, with the Lie algebra of the base Lie group. Based on this observation, we derive the 2nd order Euler–Lagrange equations on the 2nd order tangent group from the 1st order Euler–Lagrange equations on the iterated tangent group. We also present in detail the 2nd order Lagrangian dynamics on the 2nd order tangent group of a double cross product group.
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2020.103934