On the stability and integration of Hamilton-Poisson systems on so(3)*_

Adam, R, Rory, B, Holderbaum, W and Claudiu, R (2016) On the stability and integration of Hamilton-Poisson systems on so(3)*_. Rendiconti di Matematica, Serie VII, 37 (1). pp. 1-42. ISSN 2532-3350

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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.