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

Jean Pierre Francoise; Pedro Garrido; Giovanni Gallavotti

doi:10.1063/1.4794089

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arXiv · 1202.2741

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

Jean Pierre Francoise·Pedro Garrido·Giovanni Gallavotti

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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.

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Jean Pierre Francoise, Pedro Garrido, Giovanni Gallavotti. 2012-02-13. Rigid motions: action-angles, relative cohomology and polynomials with roots on the unit circle. https://doi.org/10.1063/1.4794089

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