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Yayın Second order Lagrangian dynamics on double cross product groups(Elsevier B.V., 2021-02) Oğul, Esen; Kudeyt, Mahmut; Sütlü, Serkan SelçukWe 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.Yayın Lagrangian dynamics on matched pairs(Elsevier Science BV, 2017-01) Sütlü, Serkan Selçuk; Esen, OğulGiven a matched pair of Lie groups, we show that the tangent bundle of the matched pair group is isomorphic to the matched pair of the tangent groups. We thus obtain the Euler–Lagrange equations on the trivialized matched pair of tangent groups, as well as the Euler–Poincaré equations on the matched pair of Lie algebras. We show explicitly how these equations cover those of the semi-direct product theory. In particular, we study the trivialized, and the reduced Lagrangian dynamics on the group SL(2,C).
