It is cylindrical in shape and is solid (not hollow) and has uniform density. Igonre air resistance. It spins with some angular velocity omega and spins in the other possible ways. Apart from omega, how many more degrees of freedom is possible? I can find the MOI of a rod spinning with just angular velocity omega on a horizontal table, and hence the Lagrangian (and Hamiltonian). But what about with these extra DOF? I'm not familiar with working out the MOI for more than 1 DOF. Thanks for your help in advance.