Regular and Chaotic Dynamics

, Volume 14, Issue 2, pp 223–236 | Cite as

Explicit solution of the Zhukovski-Volterra gyrostat

  • I. BasakEmail author
Research Articles


The paper is devoted to explicit integration of the classical generalization of the Euler top: the Zhukovski-Volterra system describing the free motion of a gyrostat. We revise the solution for the components of the angular momentum first obtained by Volterra in [1] and present an alternative solution based on an algebraic parametrization of the invariant curves. This also enables us to derive an effective description of the motion of the body in space.

Key words

rigid body dynamics explicit integration elliptic curves 

MSC2000 numbers

37J60 37J35 70H45 


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Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.Department de Matemàtica Aplicada IUniversitat Politecnica de CatalunyaBarcelonaSpain

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