Geodesic
Tulczyjew's Triplet for Lie Groups. II: Dynamics
Ogul Esen1 ; Hasan Gümral2
1Dept. of Mathematics, Gebze Technical University, 41400 Gebze -- Kocaeli, Turkey
2Dept. of Mathematics, Australian College, 13015 Safat, Kuwait
Journal of Lie Theory, Tome 27 (2017) no. 2, pp. 329-356

Voir la notice de l'article provenant de la source Heldermann Verlag

Taking configuration space as a Lie group, the trivialized Euler-Lagrange and Hamilton's equations are obtained and presented as Lagrangian submanifolds of the trivialized Tulczyjew's symplectic space. Euler-Poincaré and Lie-Poisson 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.
Classification : 22E65, 22E60, 22E70, 37E65, 70K65, 70H03, 70H05
Mots-clés : Trivialized Euler-Lagrange equations, trivialized Hamilton's equations, Euler-Poincaré equations, Lie-Poisson equations, Morse families, Tulczyjew's triplet, Legendre transformation, Lagrangian submanifold, diffeomorphisms group

Ogul Esen  1   ; Hasan Gümral  2

1 Dept. of Mathematics, Gebze Technical University, 41400 Gebze -- Kocaeli, Turkey
2 Dept. of Mathematics, Australian College, 13015 Safat, Kuwait 
Ogul Esen; Hasan Gümral. Tulczyjew's Triplet for Lie Groups. II: Dynamics. Journal of Lie Theory, Tome 27 (2017) no. 2, pp. 329-356. http://geodesic.mathdoc.fr/item/JOLT_2017_27_2_a2/
@article{JOLT_2017_27_2_a2,
     author = {Ogul Esen and Hasan G\"umral},
     title = {Tulczyjew's {Triplet} for {Lie} {Groups.} {II:} {Dynamics}},
     journal = {Journal of Lie Theory},
     pages = {329--356},
     year = {2017},
     volume = {27},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2017_27_2_a2/}
}
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