Presents Lagrangian dynamics in Lie groups, revealing new transformations and equations.
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-Poincar 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.
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Esen et al. (2017) studied this question.
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