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
DOI:10.20537/nd1203008