Second Order Lagrangian Dynamics On Double Cross Product Groups

Esen, Oğul; Kudeyt, Mahmut; Sütlü, Serkan

doi:10.48550/arxiv.1909.10375

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The Infinitesimal Group Action1

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2020

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“…where g is the Lie algebra of the Lie group G, and L g is the left translation on G. We refer [18,21,36,42,48,55,60] for some further information about the tangent group.…”

Section: The Infinitesimal Group Actionmentioning

confidence: 99%

Tulczyjew's Triplet with an Ehresmann connection I: Trivialization and Reduction

Esen¹,

Kudeyt²,

Sütlü³

2020

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A. The Tulczyjew's triplet is a geometric framework that makes the Legendre transformation available even for the singular systems. In this work we present the trivialization, in both the horizontal and the vertical terms, and the reduction of the classical triplet under a symmetry group action in the presence of an Ehresmann connection. We thus establish a geometric pathway for the Legendre transformations of singular dynamical systems after reduction.

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“…where g is the Lie algebra of the Lie group G, and L g is the left translation on G. We refer [18,21,36,42,48,55,60] for some further information about the tangent group.…”

Section: The Infinitesimal Group Actionmentioning

confidence: 99%