Journal of Lie Theory

no. 2
Tulczyjew's Triplet for Lie Groups. II: Dynamics
Journal of Lie Theory, Volume 27 (2017) no. 2, pp. 329-356
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.
DOI: 10.5802/jolt.949
Classification: 22E65, 22E60, 22E70, 37E65, 70K65, 70H03, 70H05
Keywords: 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 
@article{JOLT_2017_27_2_a2,
     author = {O. Esen and H. 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},
     doi = {10.5802/jolt.949},
     zbl = {1404.53097},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.949/}
}
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O. Esen; H. Gümral. Tulczyjew's Triplet for Lie Groups. II: Dynamics. Journal of Lie Theory, Volume 27 (2017) no. 2, pp. 329-356. doi: 10.5802/jolt.949

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