The Hannay Angles: Geometry, Adiabaticity, and an Example

Golin S, Knauf A, Marmi S (1989)

Publication Type: Journal article, Original article

Publication year: 1989


Publisher: Springer Verlag (Germany)

Book Volume: 123

Pages Range: 95--122

Journal Issue: 1


DOI: 10.1007/BF01244019


The Hannay angles were introduced by Hannay as a means of measuring a holonomy effect in classical mechanics closely corresponding to the Berry phase in quantum mechanics. Using parameter-dependent momentum mappings we show that the Hannay angles are the holonomy of a natural connection. We generalize this effect to non-Abelian group actions and discuss non-integrable Hamiltonian systems. We prove an averaging theorem for phase space functions in the case of general multi-frequency dynamical systems which allows us to establish the almost adiabatic invariance of the Hannay angles. We conclude by giving an application to celestial mechanics.

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Golin, S., Knauf, A., & Marmi, S. (1989). The Hannay Angles: Geometry, Adiabaticity, and an Example. Communications in Mathematical Physics, 123(1), 95--122.


Golin, Simon, Andreas Knauf, and Stefano Marmi. "The Hannay Angles: Geometry, Adiabaticity, and an Example." Communications in Mathematical Physics 123.1 (1989): 95--122.

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