Konstantin Tronin

    1, Universitetskaya str, Izhevsk 426034, Russia
    Institute of Computer Science


    Tronin K. G.
    The paper explores the evolution of rotation of a rigid body influenced by a constant and dissipative disturbing moments. With the assumption that the disturbing moments are small, it has been shown numerically that for almost all initial conditions the body’s motion tends asymptotically to a steady rotation around a principal axis with either largest or smallest moment of inertia. On the plane of initial conditions, the points corresponding to these two types of ultimate rotation have been shown to be distributed almost randomly.
    Keywords: disturbed motion, probabilistic phenomena, diagrams of asymptotic motion
    Citation: Tronin K. G.,  Numerical analysis of rotation of a rigid body subject to the sum of a constant and dissipative moment, Rus. J. Nonlin. Dyn., 2005, Vol. 1, No. 2, pp.  209-213
    Tronin K. G.
    Adiabatic chaos in Liouville's equations
    2005, Vol. 1, No. 1, pp.  111-122
    A system of Liouville’s equations with slowly varying time-periodic parameters is considered. The system is shown to exhibit chaotic behavior with unique features. We start with the presentation of some general theoretical methods based on the analysis of abrupt changes of adiabatic invariants and separatrix splitting and then compare theoretical results with results obtained from numeric experiments.
    Keywords: adiabatic invariant, Liouville's equations, numeric experiment
    Citation: Tronin K. G.,  Adiabatic chaos in Liouville's equations, Rus. J. Nonlin. Dyn., 2005, Vol. 1, No. 1, pp.  111-122

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