
Journal of Lie Theory 27 (2017), No. 2, 329356 Copyright Heldermann Verlag 2017 Tulczyjew's Triplet for Lie Groups. II: Dynamics Ogul Esen Dept. of Mathematics, Gebze Technical University, 41400 Gebze  Kocaeli, Turkey oesen@gtu.edu.tr Hasan Gümral Dept. of Mathematics, Australian College, 13015 Safat, Kuwait h.gumral@ack.edu.kw Taking configuration space as a Lie group, the trivialized EulerLagrange and Hamilton's equations are obtained and presented as Lagrangian submanifolds of the trivialized Tulczyjew's symplectic space. EulerPoincaré and LiePoisson equations are presented as Lagrangian submanifolds of the reduced Tulczyjew's symplectic space. Tulczyjew's generalized Legendre transformations for trivialized and reduced dynamics are constructed. Keywords: Trivialized EulerLagrange equations, trivialized Hamilton's equations, EulerPoincaré equations, LiePoisson equations, Morse families, Tulczyjew's triplet, Legendre transformation, Lagrangian submanifold, diffeomorphisms group. MSC: 22E65, 22E60, 22E70, 37E65, 70K65, 70H03, 70H05 [ Fulltextpdf (357 KB)] for subscribers only. 