1202.2741 (Jean Pierre Francoise et al.)

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

Jean Pierre Francoise, Pedro Garrido, Giovanni Gallavotti

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.

View original: http://arxiv.org/abs/1202.2741