Adiabatic invariants for rigid bodies

I Landau & Lifshitz I mechanics introduces adiabatic through Hamiltonian that is dependent on some slowly changing parameter $lambda$. After some derivation they got
$$I=frac{1}{2pi}oint pdq=const.$$
This works for objects that have momentum and coordinate for example some point objects. But how to approach adiabatic invariants in case of rigid bodies?