Geodesic
Reconstruction phases for Hamiltonian systems on cotangent bundles
Documenta mathematica, Tome 7 (2002), pp. 561-604.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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 ${\mathrm T}^*Q$ 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.
Classification : 70H33, 53D20
Keywords: mechanical system with symmetry, geometric phase, dynamic phase, reconstruction phase, Berry phase, cotangent bundle 
@article{DOCMA_2002__7__a2,
     author = {Blaom, Anthony D.},
     title = {Reconstruction phases for {Hamiltonian} systems on cotangent bundles},
     journal = {Documenta mathematica},
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     publisher = {mathdoc},
     volume = {7},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2002__7__a2/}
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Blaom, Anthony D. Reconstruction phases for Hamiltonian systems on cotangent bundles. Documenta mathematica, Tome 7 (2002), pp. 561-604. http://geodesic.mathdoc.fr/item/DOCMA_2002__7__a2/