Published January 1, 2021
| Version v1
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Second order Lagrangian dynamics on double cross product groups
Creators
- 1. Gebze Tech Univ, Dept Math, TR-41400 Gebze, Turkey
- 2. Isik Univ, Dept Math, TR-34980 Sile Istanbul, Turkey
Description
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. (c) 2020 Elsevier B.V. All rights reserved.
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