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An integrable system can be defined as a symplectic manifold together with the maxiumum possible number of Poisson commuting functions on the manifold which are almost everywhere independent. By the ...

I would like to consider the reduced Hamiltonian $n$ body problem, but am struggling with the angular momentum reduction seeing as the $SO(3)$ action is not free and the reduction is singular. ...

The classical dynamics of a rigid body in three dimensions may be described as the motion of a point on a configuration space given by the Lie group $SO(3)$, governed by Euler's equations for rigid ...