Geodesic
On quadratic integral Poincare--Zhukovsky's equations
Russian journal of nonlinear dynamics, Tome 8 (2012) no. 3, pp. 523-540

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For Poincaré–Zhukovsky's equations with non-diagonal matrices in the Hamiltonian, we obtain conditions for existence of the quadratic integral $(\mathbf{YS}, \mathbf{K}) = \mathrm{const}$ and the explisit form of it. It is shown that if the integral exists, then the equations reduce to the Schottky's case.
Keywords: Poincaré–Zhukovsky's equations, quadratic integral
Mots-clés : non-diagonal matrices, Schottky's case. 
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     author = {Vladimir Yu. Ol'shanskii},
     title = {On quadratic integral {Poincare--Zhukovsky's} equations},
     journal = {Russian journal of nonlinear dynamics},
     pages = {523--540},
     publisher = {mathdoc},
     volume = {8},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2012_8_3_a7/}
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Vladimir Yu. Ol'shanskii. On quadratic integral Poincare--Zhukovsky's equations. Russian journal of nonlinear dynamics, Tome 8 (2012) no. 3, pp. 523-540. http://geodesic.mathdoc.fr/item/ND_2012_8_3_a7/