Geodesic
Tulczyjew's triplet for Lie groups III: Higher order dynamics and reductions for iterated bundles
Theoretical and applied mechanics, Tome 48 (2021) no. 2.

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Given a Lie group $G$, we elaborate the dynamics on $T^*T^*G$ and $T^*TG$, which is given by a Hamiltonian, as well as the dynamics on the Tulczyjew symplectic space $TT^*G$, which may be defined by a Lagrangian or a Hamiltonian function. As the trivializations we adapted respect the group structures of the iterated bundles, we exploit all possible subgroup reductions (Poisson, symplectic or both) of higher order dynamics.
Keywords: Euler-Poincaré equations, Lie-Poisson equations, higher order dynamics on Lie groups 
@article{TAM_2021_48_2_a8,
     author = {O\u{g}ul Esen and Hasan G\"umral and Serkan S\"utl\"u},
     title = {Tulczyjew's triplet for {Lie} groups {III:} {Higher} order dynamics and reductions for iterated bundles},
     journal = {Theoretical and applied mechanics},
     pages = {201 - 236},
     publisher = {mathdoc},
     volume = {48},
     number = {2},
     year = {2021},
     url = {http://geodesic.mathdoc.fr/item/TAM_2021_48_2_a8/}
}
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Oğul Esen; Hasan Gümral; Serkan Sütlü. Tulczyjew's triplet for Lie groups III: Higher order dynamics and reductions for iterated bundles. Theoretical and applied mechanics, Tome 48 (2021) no. 2. http://geodesic.mathdoc.fr/item/TAM_2021_48_2_a8/