Integrals of Circulatory Systems Which are Quadratic in Momenta

被引：0
|
作者：
Valery V. Kozlov
机构：
[1] Steklov Mathematical Institute,
[2] Russian Academy of Sciences ,undefined
[3] P.G.Demidov Yaroslavl State University,undefined
[4] ,undefined
来源：
Regular and Chaotic Dynamics | 2021年 / 26卷
关键词：
circulatory system; polynomial integrals; Hamiltonian system; property of being conformally Hamiltonian; indices of inertia; asymptotic trajectories; Ziegler’s pendulum;
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学科分类号：
摘要：
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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页码：647 / 657
页数：10
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