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    Dmitriy Zotev

    400013, Lenin av.,27, Volgograd-13
    Department of Mathematics, Volgograd State Pedagogical University


    Zotev D. B.
    Consider a Hamiltonian system, restricted onto an invariant surface. Does it have an integral, which may be explicitly expressed through the equations, determining this submanifold? A simple criterion of the existence of partial integral, equal to their Poisson matrix determinant, has been found. This integral is not trivial iff the induced Poisson structure is nondegenerate at least at one point. Particularly, the submanifold is to be even-dimensional.
    Keywords: Hamiltonian system, partial integral, invariant submanifold
    Citation: Zotev D. B.,  A criterion for a Poisson matrix determinant to be a partial integral of the Hamiltonian system, Rus. J. Nonlin. Dyn., 2007, Vol. 3, No. 1, pp.  75-80
    Zotev D. B., Kharlamov M. P.
    The motion of a rigid body about a fixed point in a double constant force field is governed by a Hamiltonian system with three degrees of freedom. We consider the general case when there are no one-dimensional symmetry groups. We point out the critical points of the Hamilton function and corresponding critical values of energy. Using the Morse theory, we have found the smooth type of non-degenerate five-dimensional iso-energetic levels and find their projections onto the configuration space, diffeomorphic to a three-dimensional projective space. The analogs of classical motion possibility regions, the projections of iso-energetic manifolds onto one of the Poisson spheres, are studied.
    Keywords: rigid body, double constant force fields, iso-energetic manifolds, Poisson spheres
    Citation: Zotev D. B., Kharlamov M. P.,  Iso-energetic manifolds and motion possibility regions of rigid body in double force field, Rus. J. Nonlin. Dyn., 2005, Vol. 1, No. 1, pp.  23-31

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