Integrability and dynamics of the n-dimensional symmetric Veselova top

Luis García-Naranjo, Francesco Fassò, James Montaldi

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    We consider the the n-dimensional generalisation of the nonholonomic Veselova problem. We derive the reduced equations of motion in terms of the mass tensor of the body and determine some general properties of the dynamics. In particular we give a closed formula for the invariant measure, we indicate the existence of steady
    rotation solutions, and obtain some results on their stability.

    We then focus our attention on bodies whose mass tensor has a specific type of symmetry. We show that the phase space is foliated by invariant tori that carry quasi-periodic dynamics in the natural time variable. Our results enlarge the known cases of integrability of the multi-dimensional Veselova top. Moreover, they show that in some previously known instances of integrability, the flow is quasi-periodic without the need of a time reparametrisation.
    Original languageEnglish
    Pages (from-to)1205-1246
    Number of pages37
    JournalJournal of Nonlinear Science
    Issue number3
    Early online date5 Dec 2018
    Publication statusPublished - 2018


    • Integrability
    • Nonholonomic dynamics
    • Quasi-periodicity
    • Singular reduction
    • Symmetry


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