Second Order Lagrangian Dynamics On Double Cross Product Groups
Mathematical Physics
2020-05-19 v2 Differential Geometry
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.1909.10375,
title = {Second Order Lagrangian Dynamics On Double Cross Product Groups},
author = {Oğul Esen and Mahmut Kudeyt and Serkan Sütlü},
journal= {arXiv preprint arXiv:1909.10375},
year = {2020}
}
Comments
Revisions has been made to shorten the text... the discussion on discrete dynamics has been spared for a separate paper