On quadratic integral Poincare–Zhukovsky’s equations

    2012, Vol. 8, No. 3, pp.  523-540

    Author(s): Ol'shanskii V. Y.

    For Poincaré–Zhukovsky’s equations with non-diagonal matrices in the Hamiltonian, we obtain conditions for existence of the quadratic integral $({\bf YS},{\bf K}) = \rm{const}$ and the explisit form of it. It is shown that if the integral exists, then the equations reduce to the Schottky’s case.
    Keywords: Poincare–Zhukovsky’s equations, quadratic integral, non-diagonal matrices, Schottky’s case
    Citation: Ol'shanskii V. Y., On quadratic integral Poincare–Zhukovsky’s equations, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 3, pp.  523-540

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