Second Order Lagrangian Dynamics On Double Cross Product Groups

2019/09/23 by Oğul Esen, Esen, Oğul, Mahmut Kudeyt +3
Mathematics · Physics and Astronomy · #22E70 #70H50 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DG #math.MP #msc:22E70 #msc:70H50

paper · pdf · doi:10.48550/arxiv.1909.10375

Revisions has been made to shorten the text... the discussion on discrete dynamics has been spared for a separate paper

arxiv created 2020/05/17 · arxiv updated 2020/05/19

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.

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• Dynamics Over Homogeneous Spaces
• Some second-order partial differential equations associated with Lie groups
• On the geometry of higher-order variational problems on Lie groups