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