Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2012-02-13
Nonlinear Sciences
Exactly Solvable and Integrable Systems
26 pages, 1 figure
Scientific paper
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.
Francoise Jean Pierre
Gallavotti Giovanni
Garrido Pedro
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