# Integrals of Circulatory Systems Which are Quadratic in Momenta

*2021, Volume 26, Number 6, pp. 647-657*

Author(s):

**Kozlov V. V.**

This paper addresses the problem of conditions for the existence of conservation
laws (first integrals) of circulatory systems which are quadratic in velocities (momenta), when
the external forces are nonpotential. Under some conditions the equations of motion are reduced
to Hamiltonian form with some symplectic structure and the role of the Hamiltonian is played
by a quadratic integral. In some cases the equations are reduced to a conformally Hamiltonian
rather than Hamiltonian form. The existence of a quadratic integral and its properties allow
conclusions to be drawn on the stability of equilibrium positions of circulatory systems.

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