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Integrals of Circulatory Systems Which are Quadratic in Momenta

Integrals of Circulatory Systems Which are Quadratic in Momenta 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Regular and Chaotic Dynamics Springer Journals

Integrals of Circulatory Systems Which are Quadratic in Momenta

Regular and Chaotic Dynamics , Volume 26 (6) – Nov 1, 2021

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Publisher
Springer Journals
Copyright
Copyright © Pleiades Publishing, Ltd. 2021
ISSN
1560-3547
eISSN
1468-4845
DOI
10.1134/s1560354721060046
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Regular and Chaotic DynamicsSpringer Journals

Published: Nov 1, 2021

Keywords: circulatory system; polynomial integrals; Hamiltonian system; property of being conformally Hamiltonian; indices of inertia; asymptotic trajectories; Ziegler’s pendulum

References