The Hannay Angles: Geometry, Adiabaticity, and an Example

Golin S, Knauf A, Marmi S (1989)

Publication Type: Journal article, Original article

Publication year: 1989

Journal

Communications in Mathematical Physics Springer Verlag (Germany)

Publisher: Springer Verlag (Germany)

Book Volume: 123

Pages Range: 95--122

Journal Issue: 1

URI: http://projecteuclid.org/euclid.cmp/1104178683

DOI: 10.1007/BF01244019

Abstract

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.

Authors with CRIS profile

Andreas Knauf Lehrstuhl für Mathematik (Mathematische Physik)

Involved external institutions

Technische Universität Berlin DE Germany (DE) University of Bologna / Università di Bologna IT Italy (IT)

How to cite

APA:

Golin, S., Knauf, A., & Marmi, S. (1989). The Hannay Angles: Geometry, Adiabaticity, and an Example. Communications in Mathematical Physics, 123(1), 95--122. https://dx.doi.org/10.1007/BF01244019

MLA:

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

BibTeX: Download