Geodesic
Reconstruction phases for Hamiltonian systems on cotangent bundles
Documenta mathematica, Tome 7 (2002), pp. 561-604
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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 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.
DOI : 10.4171/dm/132
Classification : 53D20, 70H33
Mots-clés : cotangent bundle, mechanical system with symmetry, geometric phase, dynamic phase, reconstruction phase, Berry phase 
@article{10_4171_dm_132,
     author = {Anthony D. Blaom},
     title = {Reconstruction phases for {Hamiltonian} systems on cotangent bundles},
     journal = {Documenta mathematica},
     pages = {561--604},
     year = {2002},
     volume = {7},
     doi = {10.4171/dm/132},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/132/}
}
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Anthony D. Blaom. Reconstruction phases for Hamiltonian systems on cotangent bundles. Documenta mathematica, Tome 7 (2002), pp. 561-604. doi: 10.4171/dm/132

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