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Rigid motions:
action-angles, relative cohomology and polynomials
with roots on the unit circle

FM 12-01, arxiv:0812.2402, DOI://10.1063/1.3316076

Journal of Mathematical Physics, 54, 032901 (+19)

*Authors* J.P. Francoise, P.L. Garrido, G.Gallavotti

*Abstract:*
Revisiting canonical integration of the classical
solid near a uniform rotation, canonical action angle coordinates,
hyperbolic and elliptic, are constructed in terms of various power
series with coefficients which are polynomials in a variable $r^2$
depending on the inertia moments. Normal forms are derived via the
analysis of a relative cohomology problem and shown to be obtainable
without the use of ellitptic integrals (unlike the derivation of the
action-angles). Results and conjectures also emerge about the
properties of the above polynomials and the location of their roots.
In particular a class of polynomials with all roots on the unit circle
arises.

G.Gallavotti
Last modified: Thu 13 Feb 14:55:00 CEST 2010
AMS: 70E17 70E40