Hannay angle study of the Foucault pendulum in action‐angle variables

Autor:	D. F. Nelson, Alexander Khein
Rok vydání:	1993
Předmět:	Physics Classical mechanics Hannay angle Double pendulum Geometric phase law Foucault pendulum Coordinate system Solid angle General Physics and Astronomy Action-angle coordinates Polar coordinate system law.invention
Zdroj:	American Journal of Physics. 61:170-174
ISSN:	1943-2909 0002-9505
DOI:	10.1119/1.17332
Popis:	The Hamiltonian is derived for the Foucault pendulum in polar coordinates in terms of the action variables of the system. The complete solution to the Foucault pendulum is found in the small oscillation limit from the action‐angle approach. During a cycle of adiabatic change (one revolution of the earth), the polar angle change can be divided into a dynamic phase and a geometric phase, called the Hannay angle, which is independent of the duration of the adiabatic change. It is shown that the Hannay angle is equal to the solid angle swept out by the pendulum axis. Four special solutions arising from different initial conditions are considered and serve to clarify the meaning of the action variables. Other coordinate systems for which separation of variables is possible are discussed. In these doubly rotating systems, the Hannay angle is shown to vanish.
Databáze:	OpenAIRE
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