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Rendiconti di Matematica e delle sue Applicazioni
ISSN 1120-7183 (print)
ISSN 2532-3350 (online)
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On the stability and integration of Hamilton-Poisson systems on so(3)*_
ROSS MONTAGUE ADAMS - RORY BIGGS - WILLIAM HOLDERBAUM - CLAUDIU REMSING

Abstract. We consider inhomogeneous quadratic Hamilton-Poisson systems on the Lie-Poisson space so (3)*_. There are nine such systems up to affine equivalence. We investigate the stability nature of the equilibria for each of these systems. For a subclass of systems, we find explicit expressions for the integral curves in terms of Jacobi elliptic functions.

Rend. Mat. Appl. (7) 37 (2016) 1-42; pdf file pdf