Poincaré–Chetaev Equations in Dirac’s Formalism of Constrained Systems

We single out a class of Lagrangians on a group manifold, for which one can introduce non-canonical coordinates in the phase space, which simplify the construction of the Poisson structure without explicitly calculating the Dirac bracket. In the case of the SO(3) manifold, the application of this formalism leads to the Poincaré–Chetaev equations. The general solution to these equations is written in terms of an exponential of the Hamiltonian vector field.