  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\'{e} 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.
