The rigid body, though Hamiltonian, is not a symplectic dynamical system, hence does not follow the same pattern as textbook mechanics. Instead it is described by a Lie-Poisson bracket with nontrivial Casimirs. Fixing all Casimirs produces a foliation into symplectic leaves. This is discussed in detail in the Book Mechanics and symmetry by Marsden and Ratiu.

The rigid body, though Hamiltonian, is not a symplectic dynamical system, hence does not follow the same pattern as textbook mechanics. Instead it is described by a Lie-Poisson bracket with nontrivial Casimirs. These are functions with zero Poissson bracket with everything, hence constants of the motion. In general, fixing an independent set of Casimirs at a fixed value produces a foliation of the Poisson manifold into symplectic leaves. This is discussed in detail in the Book Mechanics and symmetry by Marsden and Ratiu.

The rigid body, though Hamiltonian, is not a symplectic dynamical system, hence does not follow the same pattern as textbook mechanics. Instead it is described by a Lie-Poisson bracket. This is discussed in detail in the Book Mechanics and symmetry by Marsden and Ratiu.

The rigid body, though Hamiltonian, is not a symplectic dynamical system, hence does not follow the same pattern as textbook mechanics. Instead it is described by a Lie-Poisson bracket with nontrivial Casimirs. Fixing all Casimirs produces a foliation into symplectic leaves. This is discussed in detail in the Book Mechanics and symmetry by Marsden and Ratiu.