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Adiabatic invariants for rigid bodies

Physics Asked on January 15, 2021

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?

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