Reconstruction phases for Hamiltonian systems on cotangent bundles (Q1856381)

Summary: Reconstruction phases describe the motions experienced by dynamical systems whose symmetry-reduced variables are undergoing periodic motion. A well known example is the non-trivial rotation experienced by a free rigid body after one period of oscillation of the body angular momentum vector. Here reconstruction phases are derived for a general class of Hamiltonians on a cotangent bundle \(\text{ T}^*Q\) possessing a group of symmetries \(G\), and in particular for mechanical systems. These results are presented as a synthesis of the known special cases \( Q=G\) and \( G\) Abelian, which are reviewed in detail.